A bag contains identical cards numbered 1 to 50. A card is selected randomly. Find the probability that the card selected, is :
(a) divisible by 6.
(b) not divisible by 2 and 3.
Show SolutionHide Solution↓
Given,
The bag contains identical cards numbered 1 to 50.
Total number of possible outcomes = 50
(a) Favourable outcomes = Getting a card with a number divisible by 6.
Numbers divisible by 6 = {6, 12, 18, 24, 30, 36, 42, 48}
Number of favourable outcomes = 8
By formula,
Probability = $\frac{\text{No. of favourable outcomes}}{\text{Total number of outcomes}}$
P(card divisible by 6) = $\frac{8}{50} = \frac{4}{25}$.
Hence, probability that the card selected is divisible by 6 = $\mathbf{\frac{4}{25}}$.
(b) We know that,
A number which is divisible by both 2 and 3 is divisible by 6.
∴ P(card divisible by 2 and 3) = P(card divisible by 6) = $\frac{4}{25}$
By formula,
P(card not divisible by 2 and 3) = 1 − P(card divisible by 2 and 3)
$$\begin{aligned}= 1 - \frac{4}{25} \\[1em] = \frac{25 - 4}{25}\\[1em] = \frac{21}{25}.\end{aligned}$$
Hence, probability that the card selected is not divisible by 2 and 3 = $\mathbf{\frac{21}{25}}$.