You are tossing a coin and it has a probability of p to show heads on any given toss. You keep on tossing the coin until you see a heads. Let X represent the number of tosses until you see the first heads. 1. Find the probability that X is odd. 2. Find the probability that X is even, DO NOT USE QUESTION 1.

Medenovgj 2022-09-17 Answered
Probability of Landing Heads on Certain Toss/Summing to 1.
You are tossing a coin and it has a probability of p to show heads on any given toss. You keep on tossing the coin until you see a heads. Let X represent the number of tosses until you see the first heads.
1. Find the probability that X is odd.
2. Find the probability that X is even, DO NOT USE QUESTION 1.
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Answers (1)

Cremolinoer
Answered 2022-09-18 Author has 11 answers
Step 1
P ( X 0 ( mod 2 ) ) = p n 0 ( 1 p ) 2 n + 1 = p ( 1 p ) 1 ( 1 p ) 2
P ( X 1 ( mod 2 ) ) = p n 0 ( 1 p ) 2 n = p 1 ( 1 p ) 2
Step 2
p ( 1 p ) 1 ( 1 p ) 2 + p 1 ( 1 p ) 2 = 2 p p 2 2 p p 2 = 1

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