A coin is based so that a head is twice as likely to occur as a tail. If coin is tossed 3 times, the

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14.Probability

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A coin is based 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-

A

$\frac{2}{9}$

B

$\frac{1}{9}$

C

$\frac{2}{27}$

D

$\frac{1}{27}$

(JEE MAIN-2024)

Solution

Let probability of tail is $\frac{1}{3}$

$\Rightarrow$ Probability of getting head $=\frac{2}{3}$

$\therefore$ Probability of getting $2$ tails and $1$ head

$=\left(\frac{1}{3} \times \frac{2}{3} \times \frac{1}{3}\right) \times 3$

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

$=\frac{2}{9}$

Standard 11

Mathematics

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