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A bag contains $n + 1$ coins. It is known that one of these coins shows heads on both sides, where as the other coins are fair. One coin is selected at random and tossed. If the probability that toss resulted in head is $\frac{7}{12}$ , then the value of n is

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answer is 5.

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Detailed Solution

Let A be the event that fair coin is selected and B that biased coin

$P (t o s s r e s u l t i n h e a d) =$ $P (\frac{H}{A}) + P (\frac{H}{B})$ $= \frac{7}{12} = \frac{n}{n + 1} \times \frac{1}{2} + \frac{1}{n + 1} \times 1$

$\Rightarrow n = 5$

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