If x is any number chosen from 1, 2, 3 and y is selected from the numbers 1, 4, 9, then P(xy < 9) =

Given:

x is chosen from {1, 2, 3}.

y is chosen from {1, 4, 9}.

Formula Used:

Probability, P(E) = (Number of favorable outcomes) / (Total number of outcomes)

Calculation:

Total outcomes = Number of choices for x × Number of choices for y = 3 × 3 = 9.

Favorable outcomes (xy < 9):

If x = 1: xy = 1 × 1 = 1, 1 × 4 = 4, 1 × 9 = 9 (2 values satisfy xy < 9).

If x = 2: xy = 2 × 1 = 2, 2 × 4 = 8, 2 × 9 = 18 (2 values satisfy xy < 9).

If x = 3: xy = 3 × 1 = 3, 3 × 4 = 12, 3 × 9 = 27 (1 value satisfies xy < 9).

Total favorable outcomes = 2 + 2 + 1 = 5.

Probability: P(xy < 9) = Favorable outcomes / Total outcomes.

⇒ P(xy < 9) = 5 / 9.

The probability that xy < 9 is \(\frac{5}{9}\).