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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 difference between a normal distribution and the standard normal distribution?
The standard normal distribution is a normal distribution with mean 0 and variance 1.
Given that it is a king, the probability that it is a face card is 100%. All Kings are face cards.
What is the symbol for probability of success in a binomial trial?
The symbol for probability of success in a binomial trial is the letter p. It is the symbol used for probability in all statistical testing.
If two dice are thrown what is the probability of the sum of the numbers being a seven or an eleven?
To roll a 7, it doesn't matter what your first die rolls at, as every number on the die has a complement that will add up to 7. This means that your odds on rolling 7 are actually your odds on rolling the appropriate number on the second die. ie. 1/6. No matter what your first die is, the second can potentially give you a number that brings the total to 7.
To roll an 11 however, your odds are not as high. This is because you must roll a five and a six to hit 11. Your first die can be either of the two, but your second die must be it's complement. In this case then, your odds are 2/6 * 1/6, or 1/18.
Probability of not blue is the probability of white. The probability of white is 11/(11+21) or 11/32.
Since the box contains 16 marbles, seven of them white, then the probability of drawing one white marble is 7/16. If you replace the marble and draw again, the probability of drawing another white marble is still 7/16. The net probability of drawing two white marbles, while replacing the first, is 49/256.
In craps if you play both the 6 and 8 what are your odds against rolling a 7?
In craps, the chance for rolling a 7 never changes. First roll, tenth roll - doesn't matter. The chance is always 6 out of 36 (or roughly 17%). The chance of rolling a 6 is always 5 out of 36 (or 20%). The chance of rolling an 8 is always 5 out of 36 (or 20%). The chance of hitting either a 6 or an 8 before hitting a 7 would be 10 to 6 (with the favor going towards hitting either the 6 or 8).
There are two ways to look at this problem; gender or person.
Gender (M=Male, F=Female); There is only one way and that is MFMFMFMFM.
By person, you have 9 places to fill. The first is 5 males could be placed there, the next 4 females could be placed there, the next 4 males can be placed there, the next 3 females can be placed there and so forth. So in this instance there are 5*4*4*3*3*2*2*1*1 = 2880 arrangements.
Another way is
just 5!*4!=2880.
Here 5! is for men and 4! for women.
ie. Men can be arranged in 5 ways and women can be arranged in 4 ways.
What is probability of having 0ne boy out of 3 children?
We can write the sample space for 3 children as follows (b=boy, g=girl). bbb gbb bbg gbg bgb ggg bgg ggb The sample space is 8; each has a probability of 1/8. From above, you can see 3 instances that have 1 boy; bgg, gbg & ggb. Therefore, add 1/8 + 1/8 + 1/8 = 3/8 probability one boy having three children.
What are the odds for drawing a King from a regular deck of 52 cards?
There are 4 kings and 52 cards so the probability of drawing a king are 4/52 or 2/26.
What is the area under the normal distribution curve to the right of z that equals 3.24?
0.0006 (approx).
A six-sided cube is rolled Find the probability of rolling a six?
Probability = (number of successful outcomes) / (number of possible outcomes)
Possible outcomes: 6
Successful outcomes: 1
Probability = 1/6 = 16 and 2/3 percent.
The sum of the number is even when two dice rolled?
One way to do this is to list all the possible outcomes. You can get an even sum with two even numbers or two odd numbers. So here is the list.
(1,1) (3,1)
(5,1) (2,2)
(4,2) (6,2)
(1,3) (3,3)
(5,3) (2,4)
(4,4) (6,4)
(1,5) (3,5)
(5,5) (2,6)
(4,6) (6,6)
That is 18/36 so half the time the sum will be even. Second method to calculate the probability:
Also, note that to obtain an odd sum, we need and odd number one one die and an even number on the other one. So let's use that and figure out the answer another way.
The chance of even on the first is 1/2 and odd on the second is 1/2 so the chance of even and then odd is 1/4. Now, we can also have odd on the first roll then even. That chance is also 1/4. We add these two to get 1/2 which is what we found from enumeration of the possible outcomes. This is a good example of when to add and when to multiply probabilities. When we want both and odd and an even roll, we multiply because we want two events to occur at the same time and the probability of that is less than either one by itself. This is the multiplication principle.
However, when we want to look at the probability of EITHER and odd roll followed by an even or and even followed by an odd, we must ADD. Clearly these two outcomes can not occur at the same time since the first roll must be odd or even and can't be both. This tells us the chance of an odd sum is 1/2 which means the chance of an even sum is 1-1/2 or 1/2 also. Method three:
To obtain an even sum we need either two evens or two odds. Using the logic above in method 2, we see the probability of two evens is 1/4 and of two odd is 1/4. So the probability of either one of these is 1/4+1/4=1/2
Find the probability of of guessing the top 3 winners from a group of 16 finalists?
The number of combinations from 16 finalists drawn 3 at a time is16C3, which is 560. Since only 1 of the three groups of 560 contains the winners, the probability of guessing the top 3 winners is 1/560 or 0.001786.
Why the normal distribution can be used as an approximation to the binomial distribution?
The central limit theorem basically states that for any distribution, the distribution of the sample means approaches a normal distribution as the sample size gets larger and larger. This allows us to use the normal distribution as an approximation to binomial, as long as the number of trials times the probability of success is greater than or equal to 5 and if you use the normal distribution as an approximation, you apply the continuity correction factor.
What symbol is used for probability of success in statistics?
A "p" is used for probability of success. A "q" is used for probability of failure.
What is probability of union and probability of intersection?
probablity of union
probabilty of union is define as
P(AUB)=P(A)+P(B)-P(AnB) (for not mutualy exclusive data( where atleast one event
is common in two samples)
P(AUB)=P(A)+P(B) (mutualy exculsive)
probablity of intersect
P(AnB)=P(A).P(B)
What is a listing of all possible outcomes of an experiment and the corresponding probability?
A probability assignment.
If a multiple choice test has five answers what is the probability of guessing the right answer?
You have a 50% chance of getting the right answer and a 50% of getting the wrong answer. You best bet is to eliminate your three worse/wrong answers and that leaves you with two that are more or less correct . I have taken tests where points are taken away for guessing. Each right answer was one point and for every wrong two points were taken off. This was a national standardized test. In all the testing I have taken I have no way to beat the system set up by testing. I have taken the LSAT, GRE, SAT, ACT, National Teachers Exam, and several others. Nothing beats getting the test prep book and learning the tricks for that particular test.
What is The mean of a discrete probability distribution is also called the?
The mean of a discrete probability distribution is also called the Expected Value.
What are the odds of two people having same birthday AND birthyear?
1 in 20,000!
I know 4 people with my same birthday, 3 of them not being related...
If you roll one die with 6 sides what is the probability that you will roll a 3 or a 4?
The answer is 1/3. There are six possible outcomes (1 to 6) of which two (3 or 4) are favourable so the probability is 2/6 or 1/3. In general, if A and B are two events, then Pr (A or B) = Pr(A) + Pr(B0 - Pr(A and B) [the last bit is because you are double counting those events] Here Pr(A) = Pr(3) = 1/6, Pr(B) = Pr(4) = 1/6 and Pr(A and B) = Pr(3 and 4 - simultaneously) = 0 So Pr(3 or 4) = 1/6 + 1/6 + 0 = 1/3
What is sample space for tossing 2 coins?
The sample space for tossing 2 coins is (H = Heads & T = Tails): HH, HT, TH, TT
How does a discrete probability distribution differ from a continuous probability distribution?
A discrete probability distribution is defined over a set value (such as a value of 1 or 2 or 3, etc). A continuous probability distribution is defined over an infinite number of points (such as all values between 1 and 3, inclusive).
