UPSC NDA Math Model Paper 5

Here, total number of possible outcomes N = 99 - 10 + 1 = 90.
Event is getting a prime number whose digits are also prime.
Such numbers will occur only in these ranges (because tens digit must be prime):
10 to 39 ⇒ Required prime numbers → 11, 13, 17, 23, 31, 37
50 to 59 ⇒ Required prime numbers → 53
70 to 79 ⇒ Required prime numbers → 71, 73
∴P(A)=

9

90

=

1

10