# Lesson Worksheet: Binomial Distribution Mathematics

In this worksheet, we will practice identifying binomial experiments and solving probability problems of binomial random variables.

**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?

- AGetting two numbers which sum to less than 10
- BGetting two numbers which sum to 10
- CGetting two numbers which sum to more than 10

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

- A
- B
- C
- D
- E

State the probability of a failure.

- A
- B
- C
- D
- E

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

- A is the number of times we get two numbers which sum to 10 in our 25 trials.
- B is the number of times we get two numbers which sum to more than 10 in our 25 trials.
- C is the number of times we get two numbers which sum to less than 10 in our 25 trials.

**Q4: **

Jacob is playing a game with his friend with a fair die. He will win if the die lands on 5. If Jacob plays 6 games, what is the average number of times he wins?

- A
- B5
- C1
- D
- E6

**Q5: **

When a coin is flipped 4 times, what is the probability that no tails appear? Approximate to four decimal places, if needed.

**Q6: **

A teacher asked 10 students about their birth month. What is the probability that 2Β studentsΒ were born in March? Approximate to three decimal places if needed.

**Q7: **

Which of the following is **not** true about the binomial random variable with parameters ,
the number of repetition, and , the probability of success?

- AThe variance of the binomial random variable equals .
- BThe binomial random variable is the repetition of a Bernoulli trial independent times.
- CThe probability of a success in each Bernoulli trial is the same.
- DThe average value of the binomial random variable equals .
- EThe binomial random variable is a continuous random variable.

**Q8: **

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?

- ANo
- BYes

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

- AYes
- BNo

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.