Practicing Success
The probability distribution of number of doublets in three throws of a pair of dice is |
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no. of possibilities of two dices = 6 × 6 = 36 no. of cases of doublets = 6 P(D) = P(doublet) = $\frac{6}{36} = \frac{1}{6}$ in one throw $P(\bar{D})$ = P(doublet) = $\frac{5}{6}$ in one throw X → no. of doublets in 3 throws $P(X = 0) = { }^3 C_0 \times\left(\frac{5}{6}\right)^3=\frac{125}{216}$ $P(X = 1) = { }^3 C_1 \times\left(\frac{1}{6}\right) \left(\frac{5}{6}\right)^2=\frac{25×3}{216} = \frac{75}{216}$ $P(X=2)={ }^3 C_2 \times\left(\frac{1}{6}\right)^2 \times \frac{5}{6}=\frac{15}{216}$ $P(X=2)=3 C_3 \times\left(\frac{5}{6}\right)^0 \times\left(\frac{1}{6}\right)^3=\frac{1}{216}$ Option: 1 |