Find the probability of each event. A six-sided die is rolled seven times. What is the probability that the die will show an even number at most five times?

Step-by-step explanation:

When a six sided die is rolled, the possible outcomes can be:

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

Even numbers are {2, 4, 6}

Odd Numbers are {1, 3, 5}

Probability of even numbers:

This is binomial distribution.

where probability of even numbers,  

Probability of not getting even numbers (Getting odd numbers)

Probability of getting r successes out of n trials:

Probability of getting even numbers at most 5 times out of 7 is given as:

P(0) + P(1) +P(2) + P(3) +P(4) + P(5)