Question

Cards bearing numbers 1, 3, 5, ..., 35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing
(i) a prime numbers less than 15
(ii) a number divisible by 3 and 5.

Answer 1

All possible outcomes are 1, 3, 5,...................35.
Number of possible outcomes = 18 $\left[T_n=35\Rightarrow 1+(n-1)\times 2=35\Rightarrow n=18\right]$

(i) Out of the given numbers, the prime numbers less than 15 are:

2, 3, 5, 7, 11, 13

Let E₁ be the event of getting a prime number less than 15.
Then, number of favourable outcomes = 6​
∴ P (getting a prime number less than 15) = $\frac{6}{18}=\frac{1}{3}$

(ii) Out of the given numbers, the numbers divisible by 3 and 5 are 15 and 30.
Let E₂ be the event of getting a number divisible by 3 and 5 ( such numbers will be divisible by 15). Then, number of favourable outcomes = 2​
∴ P (getting a number divisible by 3 and 5 ) = $\frac{2}{18}=\frac{1}{9}$