Four fair dice D1, D2, D3 and D4, each having six faces numbered 1,2,3,4,5, and 6, are rolled simultaneously. The probability that D4 shows a number appearing on one of D1, D2 and D3 is

Question

Four fair dice D1, D2, D3 and D4, each having six faces numbered 1,2,3,4,5, and 6, are rolled simultaneously. The probability that D4 shows a number appearing on one of D1, D2 and D3 is (A) (91/216) (B) (108/216) (C) (125/216) (D) (127/216)

Tardigrade Admin · Accepted Answer

Required probability =1-(6 ⋅ 53/64) =1-(125/216)=(91/216)

Q. 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

$\frac{91}{216}$

$\frac{108}{216}$

$\frac{125}{216}$

$\frac{127}{216}$

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

Q. Four fair dice D1​,D2​,D3​ and D4​, each having six faces numbered 1,2,3,4,5, and 6, are rolled simultaneously. The probability that D4​ shows a number appearing on one of D1​,D2​ and D3​ is

21691​

216108​

216125​

216127​