Question

From a set of 17 cards, numbered 1, 2, ..., 17, one card is drawn at random. What is the probability that number on the drawn card is a multiple of 3 or 7 ?

• A. $\frac{5}{17}$
• B. $\frac{7}{17}$
• C. $\frac{8}{17}$
• D. $\frac{6}{17}$

Answer 1

The correct option is B

$\frac{7}{17}$

The total number of possible outcomes(counting of the cards from 1 to 17) = 17

Favourable outcomes are 3, 6, 7, 9, 12, 14 and 15.
$\therefore$ No. of favourable outcomes = 7

Let $E$ be the event of getting a multiple of 3 or 7.
$\therefore$ $\text{Probability P(E)}$ = $\frac{\text{Number of outcomes favorable to E}}{\text{Number of all possible outcomes of the experiment}}=\frac{7}{17}$