Question

Five fair die are rolled. What is the probability of at most two of the dice coming up a one or a six?

Your workings should show the use of appropriate laws and formulae — do not provide a purely arithmetic answer.

Answer 1

Probability of dice coming up a one or six = Number of favorable (0 or 6) outcomes / Total outcomes

= 2 / 6

= 1 / 3

Now, here we use Binomial distribution :

where,

n = Number of trials

x = Number of success

p = Probability of success

In our case,

n = 5

p = Probability of dice coming up a one or six = 1/3

Let X denote the number of dice coming up a one or a six

Required probability =  Probability of at most two of the dice coming up a one or a six = P(X 2)

Now,

Note :

So,

Similarly,

hence,

Therefore,

Probability of at most two of the dice coming up a one or a six = 0.7901