Probability: A coin is biased so that a head is twice as likely to occur as a… | JEE Main 2024 | Yukti Vault

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JEE Main 2024 (Online) 31st January Evening ShiftQuestion 1

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

Probability

$\frac{1}{27}$$\frac{2}{27}$$\frac{1}{9}$$\frac{2}{9}$✓ Correct answer

Solution

$P(H)=2P(T)\Rightarrow P(H)=\frac23,P(T)=\frac13$. $P(\text{2T,1H})=\binom32\left(\frac13\right)^2\frac23=\frac29$. Option D.

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