A number x is selected at random from the numbers 1, 2, 3 and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16.

Question

A number x is selected at random from the numbers 1, 2, 3 and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16.

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

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Salim Ahmed Kawsar · Answer 1 · Feb 05, 2023 15:29:48

x can be any one of 1, 2, 3 or 4.
y can be any one of 1, 4, 9 or 16
Total number of cases of product of x and y = 16

Product less than 16 = (1×1, 1×4, 1×9, 2×1, 2×4, 3×1, 3×4, 4×1)
Number of cases, where product is less than 16 = 8

Required probability = 8/16 or 1/2

Salim Ahmed Kawsar · Answer 2 · Feb 05, 2023 15:29:48

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 = 8/16 = 1/2.

A number x is selected at random from the numbers 1, 2, 3 and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16.

2 Answers