3. TJ flips a fair coin two times, and Ehsaan flips a biased coin once (Ehsaan's coin lands on heads 2/3 of the time). Denote by X the total number of heads from all of TJ's and Ehsaan's flips. (i) Compute the probability P(X = 2). (ii) Compute the conditional probability that X = 2 given that TJ's first flip is a heads. (iii) Compute E[X].
3. TJ flips a fair coin two times, and Ehsaan flips a biased coin once (Ehsaan's coin lands on heads 2/3 of the time). Denote by X the total number of heads from all of TJ's and Ehsaan's flips. (i) Compute the probability P(X = 2). (ii) Compute the conditional probability that X = 2 given that TJ's first flip is a heads. (iii) Compute E[X].
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![3. TJ flips a fair coin two times, and Ehsaan flips a biased coin once (Ehsaan's coin lands on heads 2/3 of
the time).
Denote by X the total number of heads from all of TJ's and Ehsaan's flips.
(i) Compute the probability P(X = 2).
(ii) Compute the conditional probability that X = 2 given that TJ's first flip is a heads.
(iii) Compute E[X].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F732798a3-7356-4eb2-95ec-8fe8b6d34be0%2F4e549ddd-9a99-49ce-964b-2c81435528d2%2Fp2vujwj_processed.png&w=3840&q=75)
Transcribed Image Text:3. TJ flips a fair coin two times, and Ehsaan flips a biased coin once (Ehsaan's coin lands on heads 2/3 of
the time).
Denote by X the total number of heads from all of TJ's and Ehsaan's flips.
(i) Compute the probability P(X = 2).
(ii) Compute the conditional probability that X = 2 given that TJ's first flip is a heads.
(iii) Compute E[X].
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