Toss an unfair coin until we get HEAD. Suppose the total number of tosses is a random variable X, and Pr(HEAD)=p. What is the probability that X is even? Denote this event as A.

brasocas6

brasocas6

Answered question

2022-08-11

Probability that a geometric random variable is even
Toss an unfair coin until we get HEAD. Suppose the total number of tosses is a random variable X, and P r ( H E A D ) = p. What is the probability that X is even? Denote this event as A.

Answer & Explanation

Dominic Paul

Dominic Paul

Beginner2022-08-12Added 17 answers

Step 1
X is even exactly when the first toss is Tails, which happens with probability 1 p, and when the remaining number of tosses is odd, which happens with conditional probability 1 P ( A ).
Step 2
Thus, P ( A ) = ( 1 p ) ( 1 P ( A ) )

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