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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 9 cards of the same suit in one hand out of 52 cards?

Asssuming you mean in a 13 card hand, to get exactly nine cards in a suit, there are 4 x C(13,9) x C(39,4) possible hands out of C(52,13) total hands. That is 4 x 58,809,465 / 635,013,559,600 = 0.000370445412454, or about 1 in 2700.

When is it useful to use probability?

When there is uncertainty about the outcome of a trial or experiment.

What is the probability of rolling a total score of 10 or greater?

Assuming you are rolling six sided dice.

You could roll (4,6)(5,5)(5,6)(6,4)(6,5)(6,6)

6 ways / 36 total opportunities =1/6

How do you construct a probability distribution?

First decide whether the event space is discrete or continuous.

For a discrete event space, for each outcome in the space assign a probability: a number in the interval [0, 1] such that the sum of probabilities for all outcomes is 1. The mapping from the event space to the probabilities is the probability distribution function.

The procedure for a continuous event space is analogous: the sum is replaced by the integral.

What is the probability of pulling two kings out of a deck of 52?

The probability of drawing two kings from a standard deck of 52 cards is (4 in 52) times (3 in 51), or 12 in 2652, or 1 in 221, or about 0.004525.

What is the probability of tossing a coin 5 times and getting at least one tail and one head?

This is one of those cases where it is probably easier to think what is the probability of not doing it, then subtracting that from 1 to get the probability of doing it. To not get at least one head and one tail, you would have to get all heads or all tails. To get all heads, the probability is (1/2)5. To get all tails is the same probability; so double it to get the probability of either of those. 2(1/2)5=1/16. Subtract the 1/16 from 1 to get 15/16. Answer: 15/16

What is the indicated z score if a graph depicts a standard normal variance with the mean 0 and standard deviation of 1?

For a N(0, 1) distribution, no linear transformation is necessary and so the z-score is the value of the coordinate on the horizontal axis.

For a N(0, 1) distribution, no linear transformation is necessary and so the z-score is the value of the coordinate on the horizontal axis.

For a N(0, 1) distribution, no linear transformation is necessary and so the z-score is the value of the coordinate on the horizontal axis.

For a N(0, 1) distribution, no linear transformation is necessary and so the z-score is the value of the coordinate on the horizontal axis.

What is the difference between independent events and mutually exclusive events?

Independent events are events which are not connected; for example, my choice of food for lunch will have no affect on your choice of a shirt to wear in the morning. Mutually exclusive events are connected. If one happens, the other can't happen. For example, let us say that you are flying an airplane and you have a choice of airports at which you can land. If you land at one airport, you will therefore not land at the other airport, because you can land at only one airport at a time (although you can still land at other airports in the future). At a given time, the events of landing at airport A and landing at airport B are mutually exclusive.

What causes objects to sink?

An object will sink if gravity effects it more then it's boyancy does.

How is probability related to statistics?

Probability is related to statistics in a direct manner. When one is doing a research for statistics, probability has to be used especially in sampling a small region.

If you are 14 what are the chances of you losing your baby?

Hi hon If you see your doctor on a regular basis I am sure everything will be just fine. I suggest you educate yourself off the web regarding how to care for yourself and your baby as well as child birth. You didn't mention parents, but it's OK to either have them with you during labor, or an aunt or just a good friend. Have someone there for you! Get going to your doctor, have a list of questions to ask him/her and they will make you feel a whole lot better. To get your information please go to: www.google.com ASK: Things to know about being pregnant. The more you learn the less fearful you will be. Good luck hon Merry Christmas Marcy it is higher then normal and thers a higher risk for low birth weight with means theres double the chance of the baby dieing within the first year but if u eat healthy and do what ur supposed to then i think u'll be ok

Does bike riding bring your period faster?

Heavy exercise in general can mess with your periods, regardless of how you exercise. Usually through delaying them or in extreme cases cause them to cease entirely. Anyhow your body isn't clockwork perfect, and periods can shift a bit for no obvious reason.

If there is a test of 12 true false questions and all answers are guessed what is the mean and standard deviation of correct answers?

We'll assume reasonably that you get a correct answer with probability 0.5.

Then the context implies that the number of correct answers is a sum of 12 Bernoulli random variables with p=0.5, which becomes a Binomial distribution with n=12 and p=0.5. Formally:

Y(i)~Ber(0.5) => X = Y(1) + ... + Y(12) => X~Bin(12,0.5)

The mean for a Binomial distribution is n*p, hence E(X)=12*0.5=6.

The variance for a Binomial distribution is n*p*(1-p), hence Var(X)=12*0.5*0.5=3.

The standard deviation is calculated as the square root of the variance so SD(X)=3^0.5=1.732.

What is the probability of getting a sum of 5 on the first toss of 2 dice and a sum of 5 on the second toss?

Two dice can come up in any one of 36 ways.

You can roll a five with:

1 + 4

4 + 1

2 + 3

3 + 2

That's 4 ways out of the 36 possibilities.

The probability of a 5 is (4/36) = (1/9) = 0.1111... ≈ 0.111 = 11.1%

The probability of rolling a 5 on the second toss is also ≈ 0.111 = 11.1%

Honest dice have no memory; they don't know how the first toss came up.

The probability of getting a 5 on both the first and second rolls is (1/9)2 = (1/81) = 0.0123456789... ≈ 0.012 ≈ 1.2% (rounded)

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