- Home
- Standard 11
- Mathematics
14.Probability
hard
Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability of a random toss resulting in head is $\frac{1}{3}$, then the probability that the experiment stops with head is.
A
$\frac{1}{3}$
B
$\frac{5}{21}$
C
$\frac{4}{21}$
D
$\frac{2}{7}$
(IIT-2023)
Solution
$\mathrm{P}(\mathrm{H})=\frac{1}{3} ; \mathrm{P}(\mathrm{T})=\frac{2}{3}$
$\text { Req. prob }=\mathrm{P}(\mathrm{HH} \text { or HTHH or HTHTHH or } \ldots \ldots .)$
$+\mathrm{P}(\mathrm{THH} \text { or THTHH or THTHTHH or } \ldots .)$
$=\frac{\frac{1}{3} \cdot \frac{1}{3}}{1-\frac{2}{3} \cdot \frac{1}{3}}+\frac{\frac{2}{3} \cdot \frac{1}{3} \cdot \frac{1}{3}}{1-\frac{2}{3} \cdot \frac{1}{3}}=\frac{5}{21}$
Standard 11
Mathematics