Question

Three unbiased coins are tossed. Provided that at least two outcomes are tails, the probability of having all three outcomes as tails is

• A. $\dfrac{1}{8}$
• B. $\dfrac{1}{4}$
• C. $\dfrac{1}{3}$
• D. $\dfrac{1}{2}$

Hint:

When calculating conditional probabilities, first identify the restricted sample space and then compute the probability within that space.

Answer 1

The Correct Option is B

The sample space for tossing 3 unbiased coins is: \[ \{TTT, TTH, THT, HTT, HHT, HTH, THH, HHH\} \] Given that at least two outcomes are tails, the possible outcomes are: \[ \{TTT, TTH, THT, HTT\} \] Thus, the probability of getting all tails ($TTT$) given that at least two tails appear is: \[ P(\text{All tails} \mid \text{At least two tails}) = \dfrac{1}{4} \] Thus, the correct answer is (B) $\dfrac{1}{4}$.