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Mathematics

Number x is chosen from -3, -2, -1, 0, 1, 2 and 3. Also, x2 ≤ 5.

Assertion(A): Probability for x2 ≤ 5 is 37\dfrac{3}{7}.

Reason(R): Probability = Favourable outcomesTotal number of outcomes\dfrac{\text{Favourable outcomes}}{\text{Total number of outcomes}}.

  1. A is true, R is false.

  2. A is false, R is true.

  3. Both A and R are true and R is correct reason for A.

  4. Both A and R are true and R is incorrect reason for A.

Probability

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Answer

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 x2 ≤ 5 = Number of favourable outcomesTotal number of outcomes=57\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}} = \dfrac{5}{7}.

∴ A is false, R is true.

Hence, option 2 is the correct option.

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