Probability
Biased Coin — Binomial Probability
nta_pyq_2024_jan
Grade 12
Question:
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
$\dfrac{2}{9}$
$\dfrac{1}{9}$
$\dfrac{2}{27}$
$\dfrac{1}{27}$
Step-by-Step Solution
Key Concept: $P(H)=2/3$, $P(T)=1/3$. $P(2T,1H)=\binom{3}{1}\cdot(2/3)\cdot(1/3)^2$.
$P=3\times\frac{2}{3}\times\frac{1}{9}=\frac{2}{9}$.
Correct Answer: 1