Bunuel wrote:
Students are playing a guessing game in which a player must randomly guess which of five options is correct. After each guess, a new set of five options is presented. A player’s turn continues as long as the player answers correctly. A player’s turn ends the first time the player guesses incorrectly. What is the probability a player’s turn will end after the player guesses three times?
(A) 0.008
(B) 0.032
(C) 0.128
(D) 0.488
(E) 0.512
The player's turn ended after 3 guesses, therefore he/she must guessed the first 2 right and the 3rd one wrong.
The probability to guess the question right: \(\frac{1}{5}\)
The probability to guess the question wrong: \(\frac{4}{5}\)
Since the turn will end immediately if the student answer incorrectly, the wrong answer must be in question 3 (no need to take order of arrangement into consideration)
\(P = \frac{1}{5}*\frac{1}{5}*\frac{4}{5} = \frac{4}{125}\)
\(\frac{4}{100}\) = 0.04, therefore \(\frac{4}{125}\) should be a little less than 0.04 => (B)