Question

20 cards are numbered from 1 to 20. One card is then drawn at random. What is the probability that the number on the card drawn is
(i) a prime number ? (ii) an odd number ?
(iii) a multiple of 5? (iv) not divisible by 3 ?

Answer 1

Clearly, the sample space is given by
`S = {1, 2, 3, 4, 5, .., 19, 20}` and, n(S) = 20.
(i) Let `E_(1) =` event of getting a prime number. Then,
`E_(1) = {2, 3, 5, 7, 11, 13, 17, 19}` and, therefore, `n(E_(1)) = 8.`
`therefore` P(getting a prime number) `= P(E_(1)) = (n(E_(1)))/(n(S)) = 8/20 = 2/5.`
(ii) Let `E_(2) =` event of getting on odd number. Then,
`E_(2) = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}` and, therefore, `n(E_(2)) = 10.`
(iii) Let `E_(3) =` event of getting a multiple of 5. Then,
`E_(3) = {5, 10, 15, 20}` and, therefore, `n(E_(3)) = 4`.
`therefore` P(getting a multiple of 5) `= P(E_(3)) = (n(E_(3)))/(n(S)) = 4/20 = 1/5.`
(iv) Let `E_(4) =` event of getting a number which is not divisible by 3.
Then, `E_(4) = {1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20}` and so, `n(E_(4)) = 14`.
`therefore` P(getting a number which is not divisible by 3)
`P(E_(4)) = (n(E_(4)))/(n(S)) = 14/20 = 7/10.`