Q. 65.0( 1 Vote )

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.

Answer :

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


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