E and F are independent events with P(E) = 1/3…

E and F are independent events with P(E) = 1/3 and P(F) = 3/5.

Question 69

MediumOriginal question

$E$ and $F$ are independent events with $P(E) = \frac{1}{3}$ and $P(F) = \frac{3}{5}$ . Match each probability in List I with its value in List II.

List I	List II
A. $P(E \cap F')$	I. $\frac{11}{15}$
B. $P(E' \cap F)$	II. $\frac{2}{15}$
C. $P(E \cup F)$	III. $\frac{1}{3}$
D. $P(E \mid F')$	IV. $\frac{2}{5}$

A-II, B-IV, C-I, D-IIICorrect answerYour answerA-IV, B-II, C-I, D-IIICorrect answerYour answerA-II, B-IV, C-III, D-ICorrect answerYour answerA-IV, B-II, C-III, D-ICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$P(E \cap F') = \frac{1}{3} \times \frac{2}{5} = \frac{2}{15}$ and $P(E' \cap F) = \frac{2}{3} \times \frac{3}{5} = \frac{2}{5}$ .
$P(E \cup F) = \frac{1}{3} + \frac{3}{5} - \frac{1}{5} = \frac{11}{15}$ ; $E$ and $F'$ are independent, so $P(E \mid F') = P(E) = \frac{1}{3}$ .

Worth noting

Complements of independent events are independent, so each piece is a product of $P(E)$ or $P(E')$ with $P(F)$ or $P(F')$ .

Concept: Complements of independent events
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsIndependent events

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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.

E and F are independent events with P(E) = 1/3 and P(F) = 3/5.

Question 69

Explanation