Lesson: Binomial Distribution Mathematics

In this lesson, we will learn how to identify binomial experiments and solve probability problems of binomial random variables.

Lesson Plan

Students will be able to

explain why a random variable is binomial or not from a given context,
identify the parameters of a binomial random variable given a context,
calculate probabilities of events for a binomial random variable using its probability distribution function,
calculate probabilities using the cumulative distribution of a binomial random variable by using either a binomial distribution table or a calculator,
calculate probabilities using the cumulative distribution of a binomial random variable involving the complement rule and/or the difference rule,
find the largest or smallest value of a binomial random variable such that the probability that variable is less than or greater than the value is smaller than a given value,
solve real-world problems involving binomial probability distributions.

Lesson Explainer

Lesson Worksheet

Q1:

Which of the following scenarios is a binomial experiment?

Q2:

Follow the steps to construct a binomial experiment to find the experimental probability of rolling two dice and obtaining two numbers which sum to more than 10.

One trial of the experiment would be rolling two dice and we will conduct 25 trials. How would we define success for each trial?

State the probability, , of a success as a fraction in its simplest form.

State the probability of a failure.

Describe the random variable in this experiment, which is binomially distributed.

Q3:

3 cards are drawn from a standard deck, and the number of aces is counted.

If the 3 cards are drawn one after the other without replacement, is the number of aces considered a binomial random variable?

If the 3 cards are drawn one after the other with replacement, is the number of aces considered a binomial random variable?

If the 3 cards are drawn one after the other with replacement, what is the probability that we get 2 aces? Approximate to four decimal places if needed.