Free Printable Binomial Distribution

1.

X is the number of heads when a fair coin is flipped 12 times

Find P(X = 4)

a)

0.12

b)

0.19

c)

0.81

d)

0.93

2.

X is the number of heads when a fair coin is flipped 12 times

Find P(X ≤ 6)

a)

0.23

b)

0.61

c)

0.39

d)

0.5

3.

Which of the following is NOT an assumption of the Binomial distribution?

a)

All trials must be independent.

b)

Each trial must be classified as a success or a failure.

c)

All trials are dependent on each other.

d)

The number of successes in the trials is counted.

4.

Choose the correct sign

'probability more than 7'

a)

P(X>7)

b)

P(X<7)

c)

P(X≥7)

d)

P(X≤7)

5.

When rolling two dice, the probability of rolling doubles is ⅙. Suppose that a game player rolls the dice five times, hoping to roll doubles. What is the probability the player gets doubles less than three times in 5 attempts?

a)

0.161

b)

0.965

c)

0.015

d)

0.997

6.

The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school. What is the probability that at least 2 of the first 10 blood donors has Type B blood?

a)

0.088

b)

0.697

c)

0.214

d)

0.303

7.

The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school.What is the probability that exactly 2 of the first 20 blood donors have Type B blood?

a)

0.316

b)

0.282

c)

0.001

d)

Not here

8.

An algebra 2 test has 6 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 6 questions, what is the probability that you get exactly 3 questions correct?

a)

0.962

b)

0.132

c)

0.831

d)

0.250

9.

Is this binomial experiment? Shuffle a deck of 52 cards. Turn over the top card. Do not replace the card. Repeat the process 5 times. Let X = the card you observe.

a)

Yes

b)

No, the trials are not independent.

c)

No, there are more than 2 outcomes

10.

When rolling a fair die 100 times, what is the probability of rolling a "4"exactly 25 times?

a)

1.0%

b)

16.7%

c)

25%

d)

2.1%

11.

In a survey, it is found that 25% of the bulbs in a particular shop are spoilt. Find the probability that out of 10 bulbs,

(a) exactly 3 bulbs are spoilt,

(b) more than 8 bulbs are in good condition.

a)

(a) 0.2613; (b) 0.2540

b)

(a) 0.2503; (b) 0.2440

c)

(a) 0.3533; (b) 0.4440

d)

(a) 0.2563; (b) 0.2540

12.

Recently, a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25 patients calling in claiming to have the flu, we are interested in how many actually have the flu.

Find the probability that at least four of the 25 patients actually have the flu.

(give your answer to 4 decimal places)

(a)

13.

Recently, a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25 patients calling in claiming to have the flu, we are interested in how many actually have the flu.

How many patients do you expect to actually have flu of the 25 patients who called?

Write the numerical value only.

(a)

14.

A binomial experiment has been set up to measure the number of successes, 𝑋, of 𝑛 trials, where the probability of success in each trial is 𝑝. State the expected number of successes.

a)

$np$

b)

$\frac{n}{p}$

c)

$np^2$

d)

$np\left(1-p\right)$

e)

$n\left(1-p\right)$

15.

In a binomial experiment, the probability of a success in each trial is 0.3, and 20 trials are performed. What is the expected number of successful trials?

(a)

16.

Chloe set up the following binomial experiment to investigate the probability of drawing a face card (jack, queen, or king) from a deck of 52 cards. She performed 25 trials and each trial consisted of randomly selecting 1 of 52 cards. A success is counted as picking a face card.

Let 𝑋 be the number of face cards selected in 25 trials. Calculate 𝑃(𝑋=6).

Give your answer to 4 decimal places.

(a)

17.

Chloe set up the following binomial experiment to investigate the probability of drawing a face card (jack, queen, or king) from a deck of 52 cards. She performed 25 trials and each trial consisted of randomly selecting 1 of 52 cards. A success is counted as picking a face card.

Let 𝑋 be the number of face cards selected in 25 trials.

Using her results, calculate the experimental probability of selecting a face card.

(give your answer as a fraction in its simplest form)

(a)

18.

Chloe set up the following binomial experiment to investigate the probability of drawing a face card (jack, queen, or king) from a deck of 52 cards. She performed 25 trials and each trial consisted of randomly selecting 1 of 52 cards. A success is counted as picking a face card.

Let 𝑋 be the number of face cards selected in 25 trials.

Find the expected number of face cards selected in 25 trials.

(Give your answer to 2 decimal places)

(a)

19.

A discrete random variable $X\sim B\left(120,\ 0.4\right)$ . Find its mean and standard deviation.

a)

46; 5.335

b)

46; 5.337

c)

48; 5.367

d)

48; 5.467

20.

What does the p stand for in the binomial probability formula?

a)

Number of trials

b)

Number of Successes

c)

Probability of Successes

d)

Probability of Failures

Binomial Distribution - Practice quiz.

Total questions: 20

Worksheet time: 30mins

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