SOLUTION: An unfair coin has probability p of landing heads up on a single flip, where 0 < p < 1. The coin is tossed seven times, and the probability that the coin lands heads up exactly t

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Question 1192893: An unfair coin has probability p of landing heads up on a single flip, where
0 < p < 1. The coin is tossed seven times, and the probability that the coin lands
heads up exactly twice is equal to the probability that the coin lands heads up
exactly three times. What is the value of p? Express your answer as a common
fraction.

Can I get help on this please? Trying to understand how to solve this? Thank you for your help and time.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The probability of heads is p; the probability of tails is (1-p).

The probability of getting 2 heads on 7 flips is C%287%2C2%29%28%28p%29%5E2%29%28%28p-1%29%5E5%29.

The probability of getting 3 heads on 7 flips is C%287%2C3%29%28%28p%29%5E3%29%28%28p-1%29%5E4%29.

The probabilities of 2 or 3 heads are the same:



21%28%28p%29%5E2%29%28%281-p%29%5E5%29=35%28%28p%29%5E3%29%28%281-p%29%5E4%29

21%281-p%29=35%28p%29
21-21p=35p
21=56p
p=21%2F56+=+3%2F8

ANSWER: p=3/8