27 cards numbered 1,2,3, , 27 are put in a box and mixed thoroughly. one person draws a card from the box. find the probability that the number on the card is (i)a prime (li) divisible by 3.
Answers
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