Q; A pair of dice are rolled 20 times.

Question

A pair of dice are rolled 20 times.

Please explain for each variable when you solve.

a) What is the probability that double sixes are rolled twice?

b) Determine the expected number of double sixes?

Answer 1

The probability of a double 6 in each roll is (1/6)^2 = 1/36

Then, in 20 rolls,

a) The chance of 2 double 6's can be found either using the formula for the binomial distribution or a statistical package.

From the formula, we get C(20,2)(1/36)^2(35/36)^(20-2) = 190*(1/36)^2(35/36)^18 = .088293

For example, in Excel, we can use =binom.dist(2,20,1/36,0) - the final value means exactly 2 and not the probability less than or equal to x. We get .088293

b) E(x) = np = 20(1/36) = 20/36 = 5/9