Question

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. $\frac{1}{27}$

Answer 1

Answer: (A)

$\frac{2}{9}$

Answer 2

Define probabilities for head and tail. Let the probability of getting a tail be $\frac{1}{3}$. Since a head is twice as likely to occur as a tail, the probability of getting a head is:

$\text{Probability of head} = 2 \times \frac{1}{3} = \frac{2}{3}.$

Calculate the probability of getting two tails and one head. The scenario "two tails and one head" can happen in three possible orders: $\\{ \text{TTH, THT, HTT} \\}$. The probability of each specific order is:

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

Thus, the probability of getting exactly two tails and one head is:

$\left( \frac{1}{3} \times \frac{1}{3} \times \frac{2}{3} \right) \times 3$ $= \frac{2}{27} \times 3 = \frac{2}{9}.$

Therefore, the answer is:

$\frac{2}{9}.$