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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
This question does not have a unique answer unless we make an additional assumption: we must know something about the relationship between the trials. For example, if we are monitoring a lightbulb for failure and the "event" consists of a working lightbulb, then the event not occurring means the lightbulb doesn't work. Let the "trials" consist of turning on the lightbulb. If the bulb fails on the first trial (chance of 1 - 3/8 = 5/8) then obviously it will not work on the second trial, either. The answer in this case would be 5/8 = 62.5%. If we assume the two trials are statistically independent, we are really saying we don't want to worry about these issues. Equivalently, the person asking the question is just telling us to multiply the probabilities (which means they are probably a teacher or a textbook and they or it are mainly concerned about your ability to multiply fractions, not about your understanding of probability). The chances of the event not occurring in each trial are 5/8. Multiplying gives 25/64 = about 39%. This is quite a bit less than 62.5%.
What is the ratio of the number of ways an event can occur to the number of possible outcomes?
The term is probability (theoretical probability), or how likely a given event is to occur.
A number cube is rolled 2 times in a row What is the probability of rolling a 3 both times?
When a number cube is rolled twice, there are 36 possible outcomes. (1,1),(1,2),....(6,6).
(3,3) occurs only once. Therefore, the probability of rolling a 3 both times is 1/36.
If you Flip four coins at once what is probability of 2 head and 3 tail?
http://wiki.answers.com/Q/If_you_Flip_four_coins_at_once_what_is_probability_of_2_head_and_3_tail" The probability of flipping four coins and getting 2 heads and 3 tails is ZERO 2 heads and 3 tails requires flipping FIVE coins.
You toss a coin 5 times and it lands on heads What will it land on the 6th time?
there is a 1/2 chance that it will land on heads and 1/2 chance it will land on tails. it dosent matter what the stats are
The probability is 0.0035
What is the probability of rolling a 7 twice in two rolls of a pair of dice?
The probability of rolling 7 once with two dice is 1 in 6, o 0.1667. The probability, then, of doing that twice in a row is 1 in 36, or 0.02778.
There is no simple answer.
First of all, the probability of boys is 0.517 not0.5.
Second, the probabilities are not independent.
If you choose to ignore these important facts, then the answer is 2/3.
If you pick only one marble from the bag, at random, it can be any one of 26 marbles. Out of these, 5 of the marbles are green. Thus, there are 26 possible outcomes out of which 5 are favourable - to the event that the marble is green. Therefore the probability of a green marble is 5/26.
The calculations become more complicated if you consider choosing a green marble in several attempt: it depends on whether or not the marbles are replaced before the next one is picked.
What is the probability of getting a total of at least 9 in a single throw of two dice?
10/36. One of the easier ways to find an answer is simply to make a table showing the possibilities of every move.
1 2 3 4 5 6
1| 2 3 4 5 6 7
2| 3 4 5 6 7 8
3| 4 5 6 7 8 9
4| 5 6 7 8 9 10
5| 6 7 8 9 10 11
6| 7 8 9 10 11 12
Based on the table, there are 36 different roll combinations, with a total of 10 combinations that are at lest 9.
What is the difference between a probability mass function and a probability density function?
The probability mass function is used to characterize the distribution of discrete random variables, while the probability density function is used to characterize the distribution of absolutely continuous random variables.
You might want to read more about this at www.statlect.com/prbdst1.htm
(see the link below or on the right)
What is the probability of choosing a spade from a deck of cards?
Since there are 13 spades and 52 cards, the probability is 13/52 or 1/4=.25
Probability that a baby will be born male?
In most industrialized countries there are about 105 boys born for every 100 girls. This number does change so it is NOT constant, but it gives you a rough idea. so 105+100=205 AND 105/205 =.512195 which is the probability of being born male.
What is the probability of getting at least 2 boys out of 3 children?
As asked - this question has no calculable answer as it depends on the genetics of the parents but ...
If we assume, to make the problem a little easier, that the odds of a boy are equal to the odds of a girl, then p(boy)=p(girl)=.5 Now, at least two boys means odd of 2 or 3 boys out of three children.
The formula for finding k successes, (let's call a boy a success ONLY because that is what we are looking for) out of n trials (births) is P(n,k)=n!/(n-k)!k! (p)^k(q)^n-k ( note that the first part of this formula is 3Cn where n is 2 or 3 in this case.
So P(2,3)=3x2x1/2x1(.5)^2(.5) =3(.25)(.5)=.375 and P(3,3)=3x2x1/3x2x1(.5)^3(.5)^0 =.125 Now add these two probabilities .375+.125=.5
You could also just do a tree, with just the three children:
B.G
/ \
B.G B.G
/ . | . | . \
B.G B.G B.G B.G
The first row is the first child, then if it's a boy, look to the left half. If the first one is a girl, look to the right half. So for 3 boys, follow the very left-hand path (B-B-B).
There are 4 possibilities that yield 2 or more boys (out of the 8 total possibilities). These are {BBB, BBg, BgB, gBB}. I bolded the bottom-row ones that are the path to 2 or more boys. Probability = 4/8 = 0.5, or 50%. Doing this validates that the first method is correct (the graphical method becomes unwieldy when more events are added).
One important rule to use in any problem that asks at least is the complement rule.
The idea is simple. P(No boys )+ P( 1 boy) + P(2 boys) + P(3 boys)=1 since those are all the possible outcomes. We subtract P( No boys) and P(1 boy ) from both sides and we have
P(at least 2)=1-P(none)-P(1). In this case no boys means GGG and the chance of that is
(1/2)^3 or 1/8. Also one Girl can be GBB, BGB or BBG and each has a 1/8 chance so the three together have a 3/8 chance. This means P( as least two boys)= 1-1/8-3/8 or 1-4/8=4/8 or 50%
The "at least method is very useful when looking at large numbers of outcomes. For example, chance of at least 1 boy in 100 children. The tree would be hard to make and the binomial formula would take a long time to use. However 1-P(none) would give you the answer in a minute. It is 1-(1/2)^100.
How do you find the sample space of tossing a coin 5 times?
You think of each toss as having heads or tails, so there are two choices. If you toss the coin twice you have 4 choices HH, TT, HT and TH. The number of different coin tosses is 2n ordered tosses and n+1 unordered. For example in two tosses, 22=4 ordered tosses if HT is different than TH and if HT is the same as TH then we have 2+1=3 different possible tosses. So using this if we toss a coin 5 times and order does not matter, there are 6 different possibilities. These are HHHHH, TTTTT, HTTTT, HHTTT, HHHTT, HHHHT,HHHHH.
If order matters, there are 25=32 different possible ways to toss a coin 5 times. For example, HHHHT is different than THHHH. I will not write them all out, but you can do it easily by starting with HHHHH and changing each H to a T then two H to T and then 3, etc.
What is the probability of drawing a diamond from a deck of 52 cards?
13/52 or 1/4 (25%)
Sample Space: Ace,2,3,4,5,6,7,8,9,10,Jack,Queen,King.
The answer depends on whether or not a vehicle being a truck and a vehicle being yellow are independent. Real life suggests that they are not independent events. Consequently, there is insufficient information to provide a useful answer.
What is the use of the Gamma distribution?
It is very frequently used in statistics. First of all, multiplying a Chi-square random variable by a constant you obtain a Gamma random variable. So, for example, most estimates of variance obtained in inferential statistics have a Gamma distribution. The Gamma distribution can also be obtained by summing exponential random variables. So, the Gamma distribution pops out in models where the exponential distribution is used (e.g. reliability, credit risk). It is also used for Internet traffic modeling.
See the StatLect entry (link below) for an introduction.
There could be many questions:
What is the probability of rolling an even number.
What is the probability of rolling an odd number.
What is the probability of rolling a number less than 4.
What is the probability of rolling a number more than 3.
What is the probability of rolling 1,4, or 6.
Basically it could be any question about the probability of rolling half of the faces.
Saying that the odds of something occurring are a to b (or a:b) means that we expect the event to occur a times for every b times it does not occur. For instance, the odds of drawing tails on a coin flip are 1 to 1, so if we repeat the experiment a very large number of times, we will have 1 occurrence of "tails" for every occurrence of "heads". The odds of getting a 5 on a dice roll are 1:5, and so on.
What is the probability of getting an even number from one roll of a number cube?
If the cube has 6 sides, 1 in 2 (3 in 6). 3:6 or 1:2 it can be rote either way. =D hope i helped.
