Binomial Experiment

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

• All trials must be independent.

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

• All trials are dependent on each other.

• The number of successes in the trials is counted.

Does the following describe a binomial experiment? If yes, identify n, p, q, and x. Cyanosis is the condition of having blueish skin due to insufficient oxygen in the blood. About 80% of babies born with cyanosis recover fully. A hospital is caring for five babies born with cyanosis. The random variable represents the babies that recover fully.

• no

• Yes. n=5, p=.8, q=.2, x= 0,1, 2, 3, 4, 5

• Yes. n=5, p=.8, q=.2, x= 1, 2, 3, 4, 5

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

• Number of trials

• Number of Successes

• Probability of Successes

• Probability of Failures

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

• Number of trials

• Number of Successes

• Probability of Successe

• Probability of Failure

Sara takes a test that has 6 multiple choice questions, where each question has four possible choices. If she randomly guesses on each question, what is the probability that she will get exactly 3 questions correct?

• 0.962

• 0.831

• 0.132

• 0.250

The American College of Obstetricians and Gynecologists reports that 32% of all births in the United States take place by Caesarian section each year. Five woman are about to give birth.

What is the binomial probability that less than 3 will have a C-section birth?

• 0.0391

• 0.1906

• 0.9609

• 0.8095

Answer explanation

Binomial Probability Formula!

n = 5

p = 0.32

q = 1 - p = 0.68

x is "less than 3", so you have to find the probability when x is 2, 1 and 0. Then add them together.

p(0) = 0.1454

p(1) = 0.3421

p(2)=0.322

So, 0.1454 + 0.3421 + 0.322 = 0.8095

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? 

• 0.088

• 0.697

• 0.214

• 0.303 

If you were to flip a coin 20 times, what is the probability you would get exactly 10 heads?

• 50%

• 17.62%

• 58.81%

• 41.19%

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?

• 0.962

• 0.132

• 0.831

• 0.250

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

• 1.0%

• 16.7%

• 25%

• 2.1%