A number is picked at random from 1 to 50. What is the probability that it is divisible by 3 or by 5 (or by both)?

\frac{3}{50}

Correct answerYour answer

\frac{1}{5}

Correct answerYour answer

\frac{23}{50}

Correct answerYour answer

\frac{8}{25}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Multiples of 3 up to 50: 16. Multiples of 5: 10.
Multiples of both, i.e. of 15: 15, 30, 45, which is 3, and they were counted twice.
Favourable $= 16 + 10 - 3 = 23$ , so probability $= \frac{23}{50}$ .

Worth noting

$\frac{8}{25}$ counts only the multiples of 3, and $\frac{1}{5}$ only the multiples of 5. $\frac{3}{50}$ counts only those divisible by both.

Ten questions from Counting and Basic Probability, at your own pace.

Explanation