10 normal six sided dice are thrown. Find the probability of obtaining at least 8 failuresif a success is 5 or 6.

0.2992 = 29.92% probability of obtaining at least 8 failures.

Step-by-step explanation:

For each dice, there are only two possible outcomes. Either a failure is obtained, or a success is obtained. Trials are independent, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

A success is 5 or 6.

A dice has 6 sides, numbered 1 to 6. Since a success is 5 or 6, the other 4 numbers are failures, and the probability of failure is:

10 normal six sided dice are thrown.

This means that

Find the probability of obtaining at least 8 failures.

This is:

So

Then

0.2992 = 29.92% probability of obtaining at least 8 failures.