A pair of dice is thrown 3 times. If getting a doublet is considered a success, then the probability of two successes is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{5}{72}\)
A doublet is (1, 1), (2, 2), …, (6, 6): 6 outcomes out of 36.
\( \displaystyle p = P(\text{success}) = \frac{6}{36} = \frac{1}{6} \)
\( \displaystyle q = 1 - p = \frac{5}{6} \)
The three throws are independent. Exactly two successes means two doublets and one non-doublet, and the non-doublet can be in any of the 3 throws (\(^{3}C_{2} = 3\) ways):
\( \displaystyle P(2 \text{ successes}) = 3 \times \left(\frac{1}{6}\right)^2 \times \frac{5}{6} \)
\( \displaystyle = \frac{15}{216} = \frac{5}{72} \)