The probability distribution of the **number of doublets** in three throws of a pair of dice is:
A$P[X=0]=1/6, P[X=1]=2/6, P[X=2]=2/6, P[X=3]=1/6$
B$P[X=0]=1/216, P[X=1]=15/216, P[X=2]=75/216, P[X=3]=125/216$
CUniform over $\{0, 1, 2, 3\}$
D$P[X=0]=125/216, P[X=1]=75/216, P[X=2]=15/216, P[X=3]=1/216$
Answer & Solution
Correct answer: D. $P[X=0]=125/216, P[X=1]=75/216, P[X=2]=15/216, P[X=3]=1/216$
Binomial with $n=3$, $p=1/6$, $q=5/6$: $P[X=k] = \binom{3}{k}p^k q^{3-k}$. $P[0] = (5/6)^3 = 125/216$. $P[1] = 3(1/6)(5/6)^2 = 75/216$. $P[2] = 3(1/6)^2(5/6) = 15/216$. $P[3] = (1/6)^3 = 1/216$.
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