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

The Correct Option is A

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:

\[ \frac{2}{9}. \]