Question

A number x is selected at random from the number 1 2 3 and 4. Another number y is selected at random from the number 1 4 9 and 16. Find the probability that the product of x and y is less than 25. Please answer stepwise.

Answer 1

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