Question

Number (x) is chosen from −3, −2, −1, 0, 1, 2 and 3. Also, \[x^{2} \leq 5\].

Assertion (A): Probability for \[x^{2} \leq 5\] is \[\frac{3}{7}\].

Reason (R): Probability \[ =\frac{\text { Favourable outcomes }}{\text { Total number of outcomes }}\]

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

A is false, R is true.

Explanation: 

Number x is chosen form −3, −2, −1, 0, 1, 2 and 3. Also, x² ≤ 5.

We need to find the values of x for which x² ≤ 5.

(−3)² = 9 (not favourable)

(−2)² = 4 (favourable)

(−1)² = 1 (favourable)

0² = 0 (favourable)

1² = 1 (favourable)

2² = 4 (favourable)

3² = 9 (not favourable)

The favorable outcomes are −2, −1, 0, 1, 2 in total 5 favourable outcomes.

By formula; the probability for \[x^2 \le 5 = \frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}} = \frac{5}{7}.\]

∴ A is false, R is true.