alleryStart learning →A pair of dice is thrown 4 times. 'Getting a doublet' is a success. The probability of **exactly 2 successes** is:
- $25/216$
- $25/216$
- $6 \cdot (1/6)^2 \cdot (5/6)^2 = 150/1296 \approx 0.116$
- Cannot be determined
Show answer and solution
Correct answer: C. $6 \cdot (1/6)^2 \cdot (5/6)^2 = 150/1296 \approx 0.116$
Doublet probability $p = 6/36 = 1/6$. $n = 4$.
$P(X = 2) = {}^4C_2 (1/6)^2 (5/6)^2 = 6 \cdot (1/36)(25/36) = 150/1296 = 25/216 \approx 0.116$.