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 number less than 15.
(ii) a number divisible by 3 and 5

Answer 1

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Cards Numbered from 1 - 35
A card is drawn at Random

Let n(S) represents the Total No. of outcomes
$\implies n(S) = 35$

(1)
Prime Number less than 15 : 2,3,5, 7, 11, 13
No. of prime No.s less than 15 gives n(E)

n(E) represents favourable outcomes
$\implies$n(E) = 6

We have,
Probability = $\frac{n(E)}{n(S)}$
P(E) = $\frac{6}{35}$



(2)
Numbers divisible by 3 : 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33.

Numbers divisible by 5 : 5, 10, 15, 20, 25 , 30

Numbers divisible by 3 and 5 : 15, 30

Number of Numbers divisible by 3 and 5 in between in between 1 and 35 is n(E)
$\implies$n(E) = 2

We have,
Probability = $\frac{n(E)}{n(S)}$
P(E) = $\frac{2}{35}$

Answer 2

Step-by-step explanation:

here is the correct answer