Assertion (A): Two balls are drawn one after the other, without replacement, from a bag of 4 red and 4 blue balls. The probability that both are red is $\frac{1}{4}$ .
Reason (R): $P(E \cap F) = P(E)\,P(F \mid E)$ for any events $E$ and $F$ with $P(E) > 0$ .

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

R is the multiplication theorem: true.
By it, both are red with probability $\frac{4}{8} \times \frac{3}{7} = \frac{3}{14}$ , not $\frac{1}{4}$ : A is false.

Worth noting

$\frac{1}{4} = \frac{1}{2} \times \frac{1}{2}$ puts the first ball back before the second draw.

Concept: The multiplication theorem
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsThe multiplication theorem

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

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