Given that the student studies Physics or is a…

Given that the student studies Physics or is a boy, what is the probability that the student is a girl?

Question 29

HardOriginal question

A group of 60 students has 36 girls and 24 boys. Of the girls, 20 study Physics; of the boys, 8 study Physics. One student is picked at random from the group.

Given that the student studies Physics or is a boy, what is the probability that the student is a girl?

\frac{5}{13}

Correct answerYour answer

\frac{5}{11}

Correct answerYour answer

\frac{3}{5}

Correct answerYour answer

\frac{5}{7}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Physics or a boy: $28 + 24 - 8 = 44$ students, the 8 boys who study Physics counted once.
The girls among them are the 20 who study Physics: $\frac{20}{44} = \frac{5}{11}$ .

Worth noting

$\frac{5}{13} = \frac{20}{52}$ counts the 8 boys who study Physics twice.

Concept: Conditional probability by counting
Typical timeTypical: 150 s
Your timeYours: —

The rule this testsConditional probability

Practise this chapter →

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.

Given that the student studies Physics or is a boy, what is the probability that the student is a girl?

Question 29

Explanation