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# 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 = a_{n} = 90

a_{n} = 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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PREVIOUSA box contains cards bearing numbers 6 to 70. If one card is drawn at random from the box, find the probability that it bears (i) a one-digit number, (ii) a number divisible by 5, (iii) an odd number less than 30, (iv) a composite number between 50 and 70.NEXTTickets numbered 2, 3, 4, 5, ..... 100, 101 are placed in a box and mixed thoroughly. One ticket is drawn at random from the box. Find the probability that the number on the ticket is(i) an even number(ii) a number less than 16(iii) a number which is a perfect square(iv) a prime number less than 40.

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