Question

Assertion (A): If three coins are tossed simultaneously then the probability of getting at most one tail is \[\frac{1}{2}\].

Reason (R): Each of the three coins can show either of the two possibilities, i.e., head or tail.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

Explanation:

Step 1 – Assertion: A is true. There are 8 equally likely outcomes and 4 have at most one tail: HHH, HHT, HTH and THH. Thus, the probability is \[\frac{4}{8} = \frac{1}{2}.\]

Step 2 – Reason: R is true. Each coin has two possible outcomes, head or tail.

Step 3 – Link: R helps determine the total number of outcomes, but does not by itself identify the favourable outcomes or establish the probability in A.