Question

A bag contains 20 cards numbered from 1 to 20 one card is drawn from the bag. Find the
probability that it bears (i) a prime number (ii) a number multiple of 6.

Answer 1

Solution(i):
Let E be event of drawing a card with number divisible by 2 or 3 from the cards with numbers 1 to 20

Numbers divisible by 2 or 3 from 1 to 20=2,3,4,6,8,9,10,12,14,15,16,18,20

No. of favorable outcomes=13
Total no. of possible outcomes =20

We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
​
=
20
13
​


Therefore, the probability that a number on the card selected from numbers 1 to 20 divisible by 2 and 3 is
20
13
​


Solution(ii):
Let F be event of drawing a card with prime number from the cards with numbers 1 to 20

Prime numbers from 1 to 20=2,3,5,7,11,13,17,19

No. of favorable outcomes=8
Total no. of possible outcomes =20

We know that, Probability P(F) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
​
=
20
8
​
=
5
2
​


Therefore, the probability that a card with prime number is selected from numbers 1,2,3,...,20 =
5
2
​