. A box contains 20 cards numbered from 1 to 20 A card is drawn at random from the box .find the probability that the number on the drawn is
1)divisible by 3
2) a prime number
3)a perfect square number
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Asked on November 22, 2019 by
Belal Bhasin
A box contains 20 cards numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is
(i) divisible by 2 or 3 (ii) a prime number
Answer
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
Step-by-step explanation:
Total outcomes = 20
(1) No's divisible by 3 from 1 to 20
3,6,9,12,15,18
n = 6
P(divisible by 3) = 6/20 = 3/10
(2) Prime no's from 1 to 20
2,3,5,7,11,13,17,19
n = 8
P(prime no.) = 8/20 = 2/5
(3) Perfect squares from 1 to 20
1,4,9,16
n = 3
P(perfect square) = 4/20 = 1/5