Questions tagged [probability]

For questions about probability. independence, total probability and conditional probability. For questions about the theoretical footing of probability use [tag:probability-theory]. For questions about specific probability distributions, use [tag:probability-distributions].

The probability that an event occurs is a number in the interval $[0, 1]$, which represents how likely the event is to happen. $0$ indicates it will never happen, $1$ indicates it will always happen.

For example, throwing two dice gives a total of $6$ five times out of thirty-six. We write $$P(X=6)=\frac{5}{36}$$.

Use this tag for basic questions about probability, independence, total probability and conditional probability.

For questions about the theory of probability, use instead. For questions about specific probability distributions, use .

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N tosses of a coin ,what is the probability that number of heads are even?

We have a coin with probability of head is p and probability for tail is (1-p). We toss the coin N times, what is the probability that the number of tosses that show head is even? What I've tried is to sum over all even k's (k= 0,2,4,...) and to sum…
Shmoopy
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Two Pairs Poker Hand Probability

The probability of getting a hand with two pairs in poker is $C^{13}_2 \cdot C^4_2 \cdot C^4_2 \cdot 11 \cdot C^4_1.$ When I first started calculating the probability, I thought it was: $$\binom{13}{1} \times \binom{4}{2} \times \binom{12}{1} \times…
Quaxton Hale
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A pair of unbiased dice are rolled together till a sum of either 5 or 7 is obtained, find the probability that 5 comes before 7

Problem : A pair of unaiased dice are rolled together till a sum of either 5 or 7 is obtained, find the probability that 5 comes before 7. My approach : Probability P(A) of getting 5 as sum on two dice is $$P(A) = \frac{4}{36} =…
Sachin
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probability that point is within triangle formed by three lines of bearing

This is a basic probability problem, and I can get the solution. But for a while I was using a wrong approach. My question for the forum is why my initial approach was wrong. The problem: You're on a ship sailing off a coast in a 2-dimensional…
James
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What is the probability of exactly two out of n persons sharing a birthday?

The classical Birthday problem asks for the probability of at least two out of $n$ people sharing the same birthday or sometimes for the least amount $n$ of people required such that with a probability of 50% at least two of them share their…
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Conditional Probability injection-molding

I thought about this questions for a while now. I understand the fact that the foreman forgets to shut up the injection is 0.48. then the questions confuses me when they to tell us the probability of the defective molding will be produced 0.04 to…
KGTW
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Probability of drawing all red balls before any green ball

Question: Suppose that a box contains $r$ red balls, $g$ green balls, and $b$ blue balls. Suppose also that balls are drawn from the box one at a time, at random, without replacement. What is the probability that all $r$ red balls will be…
Silent
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probability of flipping a total of 20 heads before flipping 10 tails in a row?

I want to find the probability that I will flip a fair coin and get $10$ heads in a row before I flip a total of $20$ tails. Or the opposite, the probability that I will flip a total of $20$ heads before I flip $10$ tails in a row. I would like to…
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how is the probability of event will be affected by its successive events ??

There is a deck of 52 card. 1 card fall down. Then we take 2 cards from the rest. These 2 cards are spade. What is the probablity of that fallen card is spade?? I think answer should be $\frac 14$ ... ??
T.J.
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Expected Value of Number of Tails Minus Number of Heads

I have the following problem where, given $X_n$ is a random variable that equals the number of tails minus the number of heads when n fair coins are flipped, what is the expected value of $X_n$? I am having a difficulty getting started on this…
user93189
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Probability of murdering a guinea pig in system of 4 rooms

A guinea pig is in a system of 4 rooms as described in the following illustration (where the dolphin is the guinea pig and skull the choking poison): The guinea pig can move right in probability $p$ and left in probability $q=1-p$. In room 1 the…
user65985
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Probability of student getting 100 in a test given some conditions

A student which knows nothing, went to a test includes 6 questions with answers 'yes' or 'no' only. Find the probability that: a.The student got 100 b.The student got 100 if he knew there are 3 question with answer yes and 3 with answer no. c.The…
user65985
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Probability of infinite coin toss where tossing stops only if the number of heads is twice the number of tails

The coin is tossed until the number of heads is exactly equal to twice the number of tails. The coin lands on heads with probability . What is the probability that a coin will be tossed forever? A similar problem (A coin lands heads with probability…
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Did my TA make a mistake regarding probabilities?

So I had an assignment due yesterday, regarding the probability of the attackers second highest dice roll, being strictly bigger than the defenders second highest dice roll, in the game Risk. In the game, the attacker has three dices and the…
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Probability of winning a circular ball game

Context: You and 4 other people are sitting in a circle. You are given a ball to start the game. Every second of this game, the person with the ball has three choices they can make. They can either pass the ball to the left, pass the ball to the…