Numbers are selected at random, one at a time from the two-digit numbers 00,01,02 , -------, 99 with replacement. An event E occurs only if the product of the two digits of a selected number is 24 . If four numbers are selected, then probability, that the event E occurs at least 3 times, is

Step-by-step solution

Two-digit numbers from 00 to 99 comprise 100 distinct outcomes. We seek the probability that the product of the digits equals 24 . Let the number be represented as 10a + b where a, b 0, 1, ..., 9 . The product condition a b = 24 holds when (a, b) is (3,8) , (4,6) , (6,4) , or (8,3) , corresponding to numbers 38 , 46 , 64 , and 83 . The probability of selecting one such number is p = 4 100 = 1 25 , so q = 1 - p = 24 25 . The scenario involves n=4 independent trials. The probability of at least 3 successes is given b