Question

A coin is tossed until a head appears or until the coin has been tossed three times. Given that 'head' does not appear on the first toss, what is the probability that the coin is tossed thrice?

• A. \( \frac{1}{2} \)
• B. \( \frac{3}{8} \)
• C. \( \frac{1}{8} \)
• D. \( \frac{1}{4} \)

Hint:

When dealing with probabilities involving multiple events, break the problem into stages and calculate the probability of each event step by step.

Answer 1

The Correct Option is A

Since the coin is tossed until a head appears or after three tosses, the total possible outcomes for three tosses are as follows: - The first toss must be a tail (since we are given that 'head' does not appear on the first toss). - The second toss can either result in a head or tail. If the second toss is a head, the coin stops. If the second toss is a tail, the coin must be tossed again. For the coin to be tossed three times, both the first and second tosses must be tails, and the third toss must result in either a head or tail. The probability of this event happening is: \[ P(\text{second toss is tail and third toss occurs}) = P(\text{tail on first toss}) \times P(\text{tail on second toss}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{2}. \] Thus, the probability that the coin is tossed thrice is \( \frac{1}{2} \). Thus, the correct answer is (A).