Question

Four fair dice $D_{1}, D_{2}, D_{3}$ and $D_{4},$ each having six faces numbered $1,2,3,4,5,$ and $6,$ are rolled simultaneously. The probability that $D_{4}$ shows a number appearing on one of $D_{1}, D_{2}$ and $D_{3}$ is

• A. $\frac{91}{216}$
• B. $\frac{108}{216}$
• C. $\frac{125}{216}$
• D. $\frac{127}{216}$

Answer 1

Answer: (A)

Required probability $=1-\frac{6 \cdot 5^{3}}{6^{4}}$
$=1-\frac{125}{216}=\frac{91}{216}$