Mathematics - Probability Question with Solution | TestHub

The sequence of consecutive heads may starts with $1^{\text{st }}$ toss or $2^{\text{nd }}$ toss or $3^{\text{rd }}$ toss ---- or at $6^{\text{th }}$ toss. In any case ,if it starts with r th throw, the first (r-2) throws may be head or tail but $(\mathrm{r}-1)$ st throw must be tail, after which again a head or tail can show up: HHH ----H xxxx or xxx-----x 7 times $(r-2)(r-1)st$ $\text{ ∴ Probability }=\frac{1}{2^7}+\frac{1}{2}\cdot \frac{1}{2^7}+\frac{1}{2}\cdot \frac{1}{2^7}+\cdots +\cdots +\frac{1}{2}\cdot \frac{1}{2^7}=\frac{1}{2^7}\left[1+\frac{5}{2}\right]=\frac{7}{2^8}$ 5 times