What is the probability that the ball drawn…

What is the probability that the ball drawn from bag II is red?

Question 91

MediumOriginal question

Bag I has 3 red and 2 black balls; bag II has 2 red and 3 black balls. One ball is drawn at random from bag I and put into bag II without its colour being seen. Then a ball is drawn at random from bag II.

What is the probability that the ball drawn from bag II is red?

\frac{3}{10}

Correct answerYour answer

\frac{2}{5}

Correct answerYour answer

\frac{5}{12}

Correct answerYour answer

\frac{13}{30}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Split on the ball moved: $P(R) = \frac{3}{5} \times \frac{3}{6} + \frac{2}{5} \times \frac{2}{6}$ .
$\frac{9}{30} + \frac{4}{30} = \frac{13}{30}$ .

Worth noting

$\frac{2}{5}$ is bag II's share of red before the move; the ball moved in changes it.

Concept: The theorem of total probability
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsThe theorem of total probability

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

Practise this chapter →

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

What is the probability that the ball drawn from bag II is red?

Question 91

Explanation