Answer to Question #193612 in Statistics and Probability for Sedi

Question

In a game show, a player is asked questions one after another until they get 

one wrong, after which it is the next player’s turn. The probability that they 

get a question correct is 0.7, independent of any other question. Find the probability that the first two players are asked a total of five 

questions.

Answer 1

The following options are possible:

A) The first player will not answer the question, and the second will answer the next three questions and will not answer the fourth

$p(A) = (1 - 0.7) \cdot {0.7^3}(1 - 0.7) = 0.03087$

B) The first player will answer the first question, but not answer the second question, and the second player will answer the first 2 questions, but not answer the third

$p(B) = 0.7 \cdot (1 - 0.7) \cdot {0.7^2}(1 - 0.7) = 0.03087$

С) The first player will answer the first 2 questions, but will not answer the third question, and the second player will answer the first question, but will not answer the second question

$p(C) = {0.7^2} \cdot (1 - 0.7) \cdot 0.7 \cdot (1 - 0.7) = 0.03087$

D) The first player will answer the first 3 questions, but will not answer the fourth question, and the second player will not answer the first question

$p(D) = {0.7^3} \cdot (1 - 0.7) \cdot (1 - 0.7) = 0.03087$

Then the wanted probability is

$p = p(A) + p(B) + p(C) + p(D) = 4 \cdot 0.03087 = {\rm{0}}{\rm{.12348}}$

Answer: 0.12348