Question

A number x is selected at random from the numbers 1,4,9,16 and another number y is selected at random from the number 1,2,3,4 . find the probability that the value of xy is more then 16.

Answer 1

Hello friend

There can be on the whole 16 ways in which the numbers can be chosen

1,1 ; 1,2 ; 1,3 ; 1,4
4,1;4,2;4,3;4,4
9,1;9,2;9,3;9,4
16,1;16,2;16,3;16,4

Total possible outcomes 16

The product will be greater than 16 only in the cases
4,4
9,2;9,3;9,4
16,1;16,2;16,3;16,4

That is in 8 cases

Probability= no of favourable outcomes/total number of outcomes

=8/16

=1/2

=0.5

Hope it helps

Answer 2

Given, x = {1, 2, 3, 4}

⇒ n(x) = 4

y = {1, 4, 9, 16}

n(y) = 4

Total number of possible products

= 4 × 4 = 16.

Products x.y which are less than 16 are {1 × 1,  1 × 4, 1 × 9, 2 × 1, 2 × 4, 3 × 1, 3 × 4, 4 × 1}

n (x.y) = 8

Required probability = $\bf\huge\frac{8}{16}$ = $\bf\huge\frac{1}{2}$