Question

A coin is tossed until a head appears or it has been tossed 3 times. Given that head does not appear on the first toss, the probability that the coin is tossed 3 times is

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

Answer 1

The correct option is D $\frac{1}{2}$

Possible cases: (i) TH, (ii) TTH, (iii) TTT.
(i): $\frac{1}{2}\ast \frac{1}{2}=\frac{1}{4}$
(ii): $\frac{1}{2}\ast \frac{1}{2}\ast \frac{1}{2}=\frac{1}{8}$
(iii): $\frac{1}{2}\ast \frac{1}{2}\ast \frac{1}{2}=\frac{1}{8}$
Hence, probability $=\frac{\frac{1}{8}+\frac{1}{8}}{\frac{1}{4}+\frac{1}{8}+\frac{1}{8}}=\frac{\frac{1}{4}}{\frac{1}{2}}=\frac{1}{2}$