Binomial Probability Distributions

stats ~ the binomial probability distribution

By Jason Robart

This is known as the 10% condition for independence in sampling

Multiple Select

Which descriptions are true for a binomial distribution?

• the probability of success must be the same for each event

• the probability for each event must be 0.5

• there can be only two possible outcomes

• The probabilities must add to 1

• each trial must be independent

Multiple Choice

In a certain town, 75% of all drivers are insured. What is the expected number of insured drivers present in a group of 200 randomly selected townspeople?

• 75

• 150

• 175

• 125

Multiple Select

Which of the following could be examples of binomial probabilities? (select all that apply)

• P(success)=0.99, P(failure) = 0.01

• P(A) = 0.4, P(B) = 0.4

• P(A)= 1/3, P(B) = 1/3, P(C) = 1/3

• P(3)= 1/6, P(not 3) = 5/6

Multiple Choice

It is believed that 33% of adults HAVE NEVER read a book since graduating from high school.

If you randomly selected 500 post-high school adults, How many of them would you expect to find in that group who HAD read a book since high school?

• 335

• 33

• 165

• 67

Multiple Choice

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.

Multiple Choice

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

Multiple Choice

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 

Multiple Choice

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.

• Yes
• No, the trials are not independent.
• No, there are more than 2 outcomes

Multiple Choice

Is this binomial experiment? Shuffle a deck of 52 cards. Turn over the top card. Put the card back in the deck, shuffle again. Repeat the process 50 times. Let X = the number of aces you observe.

• Yes
• No, the trials are not independent.
• No, there are more than 2 outcomes

Multiple Choice

Which one of these variables is a binomial random variable?

• Time it takes a randomly selected student to complete a multiple choice exam
• Number of textbooks a randomly selected student bought this term 
• Number of women taller than 68 inches in a random sample of 5 women
• Number of CDs a randomly selected person owns

Multiple Choice

A test has 8 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 8 questions, what is the probability that you get at least 3 questions correct?

• 0.886

• 0.332

• 0.678

• 0.208

Multiple Choice

Binomial or Not Binomial?

Rolling a dice ten times and recording the number shown each time

• Binomial

• Not Binomial

Multiple Choice

Binomial or Not Binomial?

Rolling a dice ten times and recording how many threes are rolled

• Binomial

• Not Binomial

Multiple Choice

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

• Number of trials
• Number of Successes
• Probability of Successes
• Probability of Failures

Multiple Choice

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

• Number of trials
• Number of Successes
• Probability of Successes
• Probability of Failures

Multiple Choice

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

• Number of trials
• Number of Successes
• Probability of Successes
• Probability of Failures

Multiple Choice

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. Find the probability that the player gets doubles exactly twice in 5 attempts.

• 0.884
• 0.139
• 0.965
• 0.161