Joint Coin Probability Problem

In summary, the problem is asking for the probability that two people, A and B, playing a coin tossing game with a probability of heads (p) and tails (q=1-p) will both stop on the same number of tosses. The solution involves calculating the sum of probabilities for both A and B stopping on the same number of tosses, using a negative binomial distribution.
  • #1
FaradayLaws
8
0
Problem:
Suppose that the probability that a head appears when a coin is tossed is p and the probability that a tail occurs is q=1-p. Person A tosses the coin until the first head appears and stops. Person B does likewise. The results obtained by persons A and B are assumed to be independent. What is the probability that A and B stop on exactly the same number toss?

I am not quite sure how to solve this. I'm assuming that the tosses are distributed as a negative binomial and I'm lost as to how to put everything together.Please help !

Thanks!
 
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  • #2
Hi FaradayLaws! :smile:
FaradayLaws said:
What is the probability that A and B stop on exactly the same number toss?

It's the sum from n = 1 to ∞ of the probability that A and B both stop on the nth toss. :wink:
 

1. What is the joint coin probability problem?

The joint coin probability problem is a mathematical problem that involves determining the probability of a specific outcome when multiple coins are flipped simultaneously. It is a common problem in statistics and probability theory.

2. How is the joint coin probability problem solved?

The joint coin probability problem can be solved by using the basic principles of probability, such as the multiplication rule and the addition rule. It involves determining the sample space, calculating the total number of possible outcomes, and then calculating the probability of the desired outcome.

3. What is the difference between joint probability and conditional probability?

Joint probability refers to the probability of two or more events occurring simultaneously, while conditional probability refers to the probability of one event occurring given that another event has already occurred. In the joint coin probability problem, we are interested in the joint probability of getting specific outcomes when multiple coins are flipped at the same time.

4. Can the joint coin probability problem be applied to real-life situations?

Yes, the joint coin probability problem can be applied to real-life situations. For example, it can be used to calculate the probability of winning a lottery or the probability of getting a certain combination of outcomes in a game.

5. Are there any limitations to the joint coin probability problem?

Yes, there are limitations to the joint coin probability problem. It assumes that all coins are fair and have an equal chance of landing on either heads or tails. It also assumes that the outcomes of each coin flip are independent of each other, which may not always be the case in real-life situations.

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