Q 19 Cards marked with the numbers 2 to 101 are placed in a box and mixed thoroughly One - Maths -

Question

Q 19 Cards marked with the numbers 2 to 101 are placed in a box and
mixed thoroughly One card is drawn from this box Find the
probability that the number on the card is ( a) an even number ( b
) a number less than 14 ( c ) a number which is a perfect square (
d )a prime number less than 20

Manbar Singh · Accepted Answer

Let S be the sample space
S = {2,3,4,5,6, 100,101}
nS = 100

1 Let E be the event of getting a card bearing an even numberE = 2,
4, 6, 8, 98, 100nE = 50pE = nE nS = 50100 = 122 Let F be the event
of getting a card bearing a number less than 14F = 2, 3, 4, 5, 6,
7, 8, 9, 10, 11, 12, 13nF = 12pF = nF nS = 12100 = 3253 Let G be
the event of getting a card bearing a number that is a perfect
squareG = 4, 9, 16, 25, 36, 49, 64, 81, 100nG = 9pG = nG nS = 91004
Let H be the event of getting a card bearing a prime number less
than 20H = 2, 3, 5, 7, 11, 13, 17, 19nH = 8pH = nH nS = 8100 = 225

Q.19 Cards marked with the numbers 2 to 101 are placed in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is ( a) an even number ( b ) a number less than 14 ( c ) a number which is a perfect square ( d )a prime number less than 20.