Question

A six-sided number cube is rolled 900 times.

How many times is it expected that a number greater than 4 will be rolled?

Answer 1

Answer: Rolling a die and obtaining a number follows a binomial distribution.

Expected value of binomial distribution is

E[X]=np

where n is number of toss and p is probability of obtaining the number.

Therefore here the expected value of obtaining a number 4 is:

E[X]=900∗16=150

Step-by-step explanation:

Answer 2

It is expected that a number greater than 4 will be rolled 300 times

The sample space of a die is:

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

The probability of obtaining a number greater than 4 is:

$p = 2/6$

$p = 1/3$

In 900 rolls, the expected number of number greater than 4 is:

$E(x) = p *n$

This gives

$E(x) = 1/3 *900$

$E(x) =300$

Hence, it is expected that a number greater than 4 will be rolled 300 times

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