What is the probability of a tie when two individuals flip biased coins?

AI Thread Summary
The discussion centers on calculating the probability of a tie when a boy and girl flip biased coins with different probabilities of heads. The question lacks clarity regarding whether they stop recording after the first head appears. A suggestion is made to start with equal probabilities (e.g., p=0.5) to find the expected number of flips until heads shows up. Participants are advised to use the defined probabilities p1 and p2 to compute the desired probability. Additionally, it is recommended to post the question in a more appropriate math forum for better assistance.
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Homework Statement



boy and girl independently flip each a biased coin with probability of heads p1 for boy, and p2 for girl. they record the number of flips needed until heads shows up.

what is the probability that they tie?

Homework Equations



I just know that we should define a random variable to condition on.

The Attempt at a Solution



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First of all, the question is not clear.
"they record the number of flips needed until heads show up"
How many heads we are talking about?
do they stop recording when the first head appears?

In any case, here is hint..
why don't you start with the same probabilities for the boy and the girl, maybe with some number like (p=0.5) . Then find out the expected number of flips until a head shows up.. At this point, you'll be able to compute the desired probability.

Go back the question and plug the p_1, p_2 to get your answer
 
also you should post in the math forum, because you are in the wrong forum right now.
the forum is one level above this one and its called precalculus mathematics
 

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