Numbers are selected at random, one at a time from two digit numbers 10,11,12 ., 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, then probability that the event E occurs at least 3 times is

Step-by-step solution

Event E: Product of the two digits is 18 . array ll & E= 29,36,63,92 & p= 4 90 & q=1- 4 90 = 86 90 array Here, n=4 aligned P ( X 3) & = P ( X =3)+ P ( X =4) & = ^4 C ₃ ( 4 90 )^3 ( 86 90 )^1+ ^4 C ₄ ( 4 90 )^4 ( 86 90 )^0 & =4 ( 4 90 )^3 ( 86 90 )+1 ( 4 90 )^4 & = ( 4 90 )^4(86+1) & =87 ( 4 90 )^4 aligned