a. Determine P(X = 2), P(X = 3), and P(X = 4). b. Show that P(X = n)=(n−1)p2(1−p)n−2 for n ≥2.

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Chapter1: Combinatorial Analysis
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We throw a coin until a head turns up for the second time, where p is the probability that a throw results in a head and we assume that the outcome of each throw is independent of the previous outcomes. Let X be the number of times we have thrown the coin.

 

a. Determine P(X = 2), P(X = 3), and P(X = 4).

b. Show that P(X = n)=(n−1)p2(1−p)n−2 for n ≥2.

We throw a coin until a head turns up for the second
time, where p is the probability that a throw results in
a head and we assume that the outcome of each
throw is independent of the previous outcomes. Let X
be the number of times we have thrown the coin.
a. Determine P(X = 2), P(X = 3), and P(X = 4).
b. Show that P(X = n)=(n-1)p2(1-p)n-2 for n 22.
Transcribed Image Text:We throw a coin until a head turns up for the second time, where p is the probability that a throw results in a head and we assume that the outcome of each throw is independent of the previous outcomes. Let X be the number of times we have thrown the coin. a. Determine P(X = 2), P(X = 3), and P(X = 4). b. Show that P(X = n)=(n-1)p2(1-p)n-2 for n 22.
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