Binomial Distribution

When rolling two dice, the probability of rolling doubles is ⅙. Suppose that in a game a player rolls the dice four times, hoping to roll doubles. What is the probability the player gets doubles more than twice in 4 attempts?

• 0.016

• 0.00077

• 0.132

• 0.004

6. 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.
• The probability of success is equal to .5 in all trials.
• The number of successes in the trials is counted.

7. A Stats  test has 5 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 5 questions, what is the probability that you get exactly 2 questions correct?

• 0.6250
• 0.25
• 0.0625
• 0.2636

Mr. H, who has never really played basketball, tries to shoot a basket. It is known that he has a 10% success rate. What is the probability that he scores his second basket on his 12th throw?

• 0.0384

• 0.25

• 0.115

• 0.77

It is a little known fact that Mr. H is a world-famous poker player in his spare time. If he draws 8 cards out of a deck (with replacement), what is the probability that he gets 3 or more spades?

• 0.32

• 0.68

• 0.11

• 0.89

Seventeen people have been exposed to a particular disease. Each one independently has a 40% chance of contracting the disease. A hospital has the capacity to handle 10 cases of the disease. What is the probability that the hospital's capacity will be exceeded? 

• .965
• .035
• .989
• .011

Justin is taking a 100 question test. He has a 90 % probability of getting any one question correct. WHICH IS THE CORRECT FORMULA TO FIND OUT THE PROBABILITY that he will answer EXACTLY 70 questions correctly?

• ₁₀₀C₇₀ ( 0.18 )³⁰ ( 0.90 )⁷⁰

• ₁₀₀C₇₀ ( 0.10 )³⁰ ( 0.90 )⁶⁰

• ₁₀₀C₇₀ ( 0.10 )³⁰ ( 0.90 )⁷⁰

• ₉₉C₇₀ ( 0.10 )³⁰ ( 0.90 )⁷⁰

I throw 2 dice together and add them. I do this 60 times. What is the probability I get a score of more than 10 at least 5 times?

• 0.433

• 0.067

• 0.567

• 0.933

In a multi-choice quiz consisting of 20 questions each with 5 possible options with only 1 correct answer, what is the probability, if you are guessing, that you get more than 2 but less than 7 correct?

• 0.707

• 0.206

• 0.968

• 0.762

A fair die is rolled six times. If X denotes the number of 4s obtained, find the standard deviation of X.

• 0.962

• 0.913

• 0.831

• 0.167