Question

Denomination, one of the coins is known to have heads. He takes out one coin at random and tosses it 5 times. If it always falls with head upwards,the probability that it is double-headed coin is

• A. $\frac{32}{51}$
• B. $\frac{32}{41}$
• C. $\frac{32}{61}$
• D. $\frac{12}{41}$

Answer 1

Answer: (B)

$\frac{32}{41}$

Case1: The coin taken by the man is head-tail coin
and $5$ times haed has been obtained by tossing the coin.
The probability of this event is $\frac{9}{10}\times {\left(\frac{1}{2}\right)}^5$
Case2: It may be a head-head coin
and a head has been obtained all the five times by tossing it.
The probability of this event is $\frac{1}{10}\times {\left(1\right)}^5$
These probability are in the ratio $9:3:2$
Hence the probability that it is a head-head coin

(case$2$) is $\frac{32}{41}$.