In a quiz, 50% of the contestants answer the first question correctly, and 60% of those also answer the second correctly. In all, 12% of the contestants answer all three questions correctly. What is the probability that a contestant who answers the first two correctly also answers the third correctly?

0.2

Correct answerYour answer

0.24

Correct answerYour answer

0.3

Correct answerYour answer

0.4

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Let $Q_1, Q_2, Q_3$ be correct answers to the three questions: $P(Q_1 \cap Q_2) = 0.5 \times 0.6 = 0.3$ , and $P(Q_1 \cap Q_2 \cap Q_3) = 0.12$ .
$P(Q_3 \mid Q_1 \cap Q_2) = \frac{0.12}{0.3} = 0.4$ .

Worth noting

0.24 divides 0.12 by 0.5 alone, the chance of the first answer; the condition is both of the first two answers, with probability 0.3.

Ten questions from Conditional Probability & Bayes' Theorem, at your own pace.

Explanation