Question

Numbers are selected at random, one at a time, from the two-digit numbers 00, 01, 02, ......,99 with replacement. An event E occurs if and only if the product of the two digits of a selected number is 18. If four numbers are selected, find probability that the event E occurs at least 3 times.

Answer 1

Let E be the event that product of the two digits is 18, therefore required no. are 29, 36, 63, and 92.

Hence, p = P(E) = 4/100 and probability of non-occurrence of E is

q = 1 - P(E) = 1 - 4/100 = 96/100

Out of the four numbers selected, the probability that the event E occurs at least 3 times, is given as

P = ⁴C₃p³q + ⁴C₄p⁴

= 4(4/100)³(96/100) + (4/100)⁴ 

= 97/25⁴