Question

10 identical six-sided dice are thrown simultaneously. What is the probability of all 6 faces appearing?

Answer 1

Solution;

Suppose an experiment of throwing a dice.The sample space S is given by\

S = {1,2,3,4,5,6}

No.of elements in S are 6

probability of 6 = 1/6

Here , 10 dice are thrown.

n = 10 (No. of trials)

Let a r.v. X denotes the of 6 faces out of these 10

X follows binomial(n = 10 , p = 1/6)

The PMF of binomial is given by

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x}

Here, p = 1/6 and 1 - p = 1 - (1/6) = 5/6

Find P(all are 6)

= P(X = 10)

=  (₁₀C ₁₀) * (1/6)¹⁰ * (5/6)^10-10

⁼   (₁₀C ₁₀) * (1/6)¹⁰ * (5/6)⁰

^{= 0.0000}