A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is

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Solution

Q.
A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is [2024]

1 $\frac{2}{27}$

2 $\frac{2}{9}$

3 $\frac{1}{27}$

4 $\frac{1}{9}$

Ans.
(2)

Let $x$ be the probability of getting a tail.

$∴$ $P (T) = x; P (H) = 2 x$

$∵$ $x + 2 x = 1 \Rightarrow x = \frac{1}{3}$

$∴$ $P (T) = \frac{1}{3}$ and $P (H) = \frac{2}{3}$

$Now, required probability = {}^{3}{C_{2}} \times \frac{1}{3} \times \frac{1}{3} \times \frac{2}{3}$

$= 3 \times \frac{2}{27} = \frac{2}{9}$

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