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Probability
The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences. In mathematics, it is a measure of how often an event will happen and is the basis of statistics.
14,643 Questions
What is the probability of getting a tail if a coin is tossed twice?
75%. There are 3 possible ways of getting at least one tail from 2 tosses from a coin:
Tail & Tail or
Head & Tail or
Tail & Head
Each of these individual outcomes has a probability of 25% (e.g. the probability of getting a tail and then another tail is 25%). Adding the possible outcomes together gives you a total of 75%.
probably means that something or which is not sure .
LIKE :- I PROBABLY GET THIS ANSWER RIGHT.
We can brute-force this problem. If each man -- okay, or woman, so just pipe down, Annie Oakley -- takes one shot at the target, he'll either hit it or miss it, so there are 23 = 8 states that the target can be in when they're done shooting. Let's take a look at them. Let a one represent a hit and a zero a miss. A B C 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 Only three of those states meet the criteria stated in the question, the 4th state, the 6th one, and the 7th one. The 8th state does not count because the question said "exactly two," not "at least two." If each of the eight states had an equal probability of occurrence, we could say that the probability of any of the three two-hit states occurring would be three in eight, or 0.375. But we cannot say that because each state does not have an equal likelihood. The question says that person A will hit the target six out of seven times, so his hit probability is 6/7, and his miss probability is 1/7. B's hit probability is 4/5, and his miss probability is 1/5. C's hit probability is 3/4, and his miss probability is 1/4. So, what is the probability that the target will be in the fourth state (0 1 1) after the shooting's over? It's (1/7) * (4/5) * (3/4) = 12/140. And how about the sixth state (1 0 1)? It's (6/7) * (1/5) * (3/4) = 18/140. And the seventh (1 1 0)? It's (6/7) * (4/5) * (1/4) = 24/140. The sum of the three probabilities is 54/140 = 0.3857. So, there is about a 38.6 percent chance that the target will be struck exactly twice if each of the three men takes one shot at the target. Note that the probability that all three men will hit the target is 6*4*3/140 = 72/140 = 0.5143, so it's more likely that there will be THREE bullet holes in the target than just two. Can you figure out the probability of there being FEWER than two holes in the target?
What is the probability of getting a doublet in a single throw of two dices?
The probability of getting a number on the first dice and the same number on the second dice (e.g. a 3 and a 3) is 1/6 x 1/6 = 1/36. There are 6 ways of getting a doublet (i.e. a double 1, 2 , 3, 4, 5 or 6) so the total probability is 6 x (1/36) = 1/6.
What is the definition of theoretical probability?
Theoretical probability is the probability of an event when all outcomes are equally likely. With theoretical probability, you determine the probability by dividing the number of ways the event can occur by the total number of equally likely outcomes.
23. The probability that at least two people in a room share a birthday can be expressed more simply, mathematically, as 1 minus the probability that nobody in the room shares a birthday.
Imagine a fairly simple example of a room with only three people. The probability that any two share a birthday is :
1 - [ 365/365 x 364/365 x 363/365]
i.e. 1-P(none of them share a birthday)
=1 - [ (365x364x363) / 3653 ]
=0.8%
Similarly,
P(any two share a birthday in a room of 4 people)
= 1 - [ 365x364x363x362 / 3654 ] = 1.6%
If you keep following that logic eventually you get
P(any two share a birthday in a room of 23 people)
=1 - [(365x364x...x344x343) / 36523 ] = 51%
What is the statistical formula of the normal distribution?
y=(1/(sqrt(2*22/7)))*((e)power-((X squred)/2))
How many numbers from 1 to 100 are multiples of both 4 and 3?
Four and three share eight common multiples between 1 and 100:
12, 24, 36, 48, 60, 72, 84, 96 Remamber that zero is a multiple of all numbers.
Without getting into the mathematical details, the Central Limit Theorem states that if you take a lot of samples from a certain probability distribution, the distribution of their sum (and therefore their mean) will be approximately normal, even if the original distribution was not normal. Furthermore, it gives you the standard deviation of the mean distribution: it's σn1/2. When testing a statistical hypothesis or calculating a confidence interval, we generally take the mean of a certain number of samples from a population, and assume that this mean is a value from a normal distribution. The Central Limit Theorem tells us that this assumption is approximately correct, for large samples, and tells us the standard deviation to use.
Yes. You are measuring the number of 'successes', x, (in this case the number of heads) out of a number of 'trials', n, (in this case coin tosses) that has an assumed probability, p, (in this case 50% expressed as 0.5) of happening. This phenomenon follows a binomial distribution. Apply the binomial distribution to evaluate whether the the probability of x success from n trials with probability p of occurring is within a pre-determined 'acceptable' limit. Let's say you observe 54 heads in 100 tosses and you wonder if the coin really is fair. From the binomial distribution, the probability of getting *exactly* 54 heads from 100 tosses (assuming that the coin *is* fair & should have 0.5 chance of landing on either side) is 0.0580 or 5.8%. Note that this is not the same probability as 54 heads *in a row*. Most statisticians would agree that 5.8% is too large and conclude that the coin is fair.
What is the probability of an event occurring to the probability of an event not occurring?
the odds in favour are p/(1-p)
the odds against are (1-p)/p
What is the probability of twenty-two consecutive same gender births?
Assuming that the chance of a woman giving birth to a boy or a girl is the same (in reality there's about 105 boys born for every 100 girls) then the probability of 22 of the same gender births *in a row* is: P=(0.5)^22=0.0000002384 or 1 in 4,194,304 It depends on the "when" of the question. If you point at a childless woman, and say "She will give birth to 22 children. What is the likelyhood that they will all be girls?" In that case the probability will be one in two-to-the-twenty-second. Pretty long odds. BUT, if you point at a woman with twenty one children, and ask "What are the odds that the next one will be a girl?" Then the answer is one in two. Make sense?
The Gaussian "Bell" Curve has probability density function: f(x)= exp{-((x-mu)2/(2*sigma2)) } / (sigma*sqrt(2*pi)) where mu=mean & sigma=standard deviation
(There are, of course, many other additional characterizations.)
It is important because it tells you if the average is a very useful quantity to use to interpret the data. If someone tells you that the average person your age dies in 50 years, that seems important, but if someone says that the average person dies in 50 years, give or take 20 years, suddenly you realize there is more to the story and maybe you should save more money, just in case. Well, the "give or take" part of that statement is very useful, but not well defined. If they say the life expectancy is 50 years with a standard deviation of 20 years, then that is perfectly defined mathematically. Standard deviation is a mathematical measure of the broadness of the distribution of data.
The following two data sets, A and B, have the same mean (average):
A: 48, 49, 50, 51, 52
B: 30, 40, 50, 60, 70
The distribution of the data about the mean in A is very narrow, whereas the distribution about the mean in B is broad. The S.D. gives us a quantification of the broadness of the distribution.
In normal distributions, about 68 percent of the data will fall within one S.D. on either side of the mean. About 96 percent of the data will fall with two S.D.
Let's say your teacher gives a test to one hundred kids and the test average is 80 points and the S.D. is 10. If the distribution is "normal," about 34 kids will score between 70 and 80, and about 34 kids will score between 80 and 90. We can also predict that about 14 kids will score between 90 and 100, and 14 will score below 70. That leaves four kids. They fall into two groups: they either totally bombed the test, or they got the extra credit question to boost their score over 100!
How many outcomes are possible if a coin is tossed 10 times?
2 sides x 10 tosses, so your possibilities is 2^10 or 2x2x2x2x2x2x2x2x2x2 =1024 outcomes.
Measurements that fall beyond 3 standard deviations from the mean?
They do happen, particularly with very skewed distributions.
How can you prove that a random variable follows the Poisson distribution?
You could draw a Probability Plot: "The probability plot ... is a graphical technique for assessing whether or not a data set follows a given distribution such as the normal or Weibull. "The data are plotted against a theoretical distribution in such a way that the points should form approximately a straight line. Departures from this straight line indicate departures from the specified distribution." Source: Online Engineering Statistics Handbook http://www.itl.nist.gov/div898/handbook/eda/section3/probplot.htm
How can you state and illustrate the addition multiplication Theorem of Probability?
Addition Theorem The addition rule is a result used to determine the probability that event A or event B occurs or both occur. ; The result is often written as follows, using set notation: : ; where: : P(A) = probability that event A occurs : P(B) = probability that event B occurs : = probability that event A or event B occurs : = probability that event A and event B both occur ; For mutually exclusive events, that is events which cannot occur together: : = 0 ; The addition rule therefore reduces to : = P(A) + P(B) ; For independent events, that is events which have no influence on each other: : ; The addition rule therefore reduces to : ; Example ; Suppose we wish to find the probability of drawing either a king or a spade in a single draw from a pack of 52 playing cards. ; We define the events A = 'draw a king' and B = 'draw a spade' ; Since there are 4 kings in the pack and 13 spades, but 1 card is both a king and a spade, we have: : = 4/52 + 13/52 - 1/52 = 16/52 ; So, the probability of drawing either a king or a spade is 16/52 (= 4/13).
MultiplicationTheorem The multiplication rule is a result used to determine the probability that two events, A and B, both occur. The multiplication rule follows from the definition of conditional probability. ; The result is often written as follows, using set notation: : ; where: : P(A) = probability that event A occurs : P(B) = probability that event B occurs : = probability that event A and event B occur : P(A | B) = the conditional probability that event A occurs given that event B has occurred already : P(B | A) = the conditional probability that event B occurs given that event A has occurred already ; For independent events, that is events which have no influence on one another, the rule simplifies to: : ; That is, the probability of the joint events A and B is equal to the product of the individual probabilities for the two events.
Fermat
A bell curve is a symmetrical bell-shaped graph curve that represents the arrangement of values, how often something occurs, or probability of occurance of a set of data. It slopes downward from a point in the middle corresponding to the average also called mean value, or the maximum probability. Gather all the results of an IQ test and make a graph of them, would create a bell curve with average IQ being the mean value. The more results or values, the better the bell curve. It can be made with a line graph or a bar graph.
How do you apply ratios to probability?
Let's say you have two regular fair dice (six-sided, of course). If you throw them 360 times and keep track of the numbers you throw, you'll record a seven about 60 times. So, you could say that the ratio of all possible numbers (including sevens) to sevens to is 360 to 36 (360:60), which is the same as 6 to 1 (6:1). You could also say that the ratio of all OTHER numbers (excluding sevens) to sevens to is 300:60, or 5:1.
(there is no seven on a six sided die....)
You would have also recorded about 50 occurrences of sixes, so you could say that the ratio of sevens to sixes is 60 to 50, or 6 to 5 (6:5). Obviously, the ratio of sixes to sevens would be 5:6.
How about this:
Let's say that the probability that a certain type of rare snake will have male offspring is 0.4. Obviously, the probability of the snake's having female offspring is 0.6. If the snake has lots of offspring, the ratio of males to females will be 0.4 to 0.6, which is the same as 4 to 6, which is the same as 2 to 3 (2:3). Stated another way, for every five snakes born, two will be male, and three will be female.
By the way, whenever possible, it's a good idea to express ratios as close as you can to whole numbers, like 3:2 or 7:5. Also, whenever one of the digits is a one, it's particularly useful, like 3:1 or 9:1, or even 1.5:1. That last ratio, 1.5:1, is equal to 3:2. It depends on what you're more comfortable with.
1st George, 2nd Lisa, 3rd Jamal, 4th Susan
that guys wrong farts on a Saturday night with taco Daniels.
How do you convert a beta probability density function to a beta frequency distribution?
probability density distribution
