Question

Numberse 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. Select the correct answer from above options

Answer 1

Correct Answer - B::D Let E be the event that product of the two digits is 18, therefore required numbers are 29,3663 and 92. Hence, `pP(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 atleast 3 times, is given as `P overset(4)""C_(3)p^(3)q+overset(4)""C_(4)p^(4)` `=4((4)/(100))^(3)((96)/(100))+((4)/(100))^(4)=(97)/(25^(4))`