Cards marked with numbers 1, 3, 5, ....., 101 are placed in a bag and mixed thoroughly. A card is drawn at random from the bag. Find the probability that the number on the drawn card is (i) less than 19, (ii) a prime number less than 20.
Total numbers of elementary events are: 51
Since the common difference between the consecutive number is same: 2
It forms an A.P.
First number = a = 1
d = common difference = 3 -1 = 2
Last number = an = 90
an = a + (n-1) d
101 = 1 + (n-1)2
101 -1 = (n-1)2
100/2 = n-1
50 + 1 = n
51 = n, being number of terms
(i) Let E be the event of drawing a number less than 19
The favourable numbers are: 1, 3, 5, 7, 9, 11, 13, 15, 17,
The numbers of favourable outcomes = 9
∴ P (number less than 19) = P (E) = 9/51
(ii) Let E be the event of getting a prime number less than 20
The favourable numbers are: 2, 3, 5, 7, 11, 13, 17, 19
Then, the numbers of favourable outcomes = 8
∴ P (prime number less than 20) = P (E)= 8/51