Binomial and Geometric Random Variables

If you want a certain number of successes in a set amount of trials, use the ????? model.

• geometric

• binomial

• normal

• calculato

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? (Hint: It may help to use the complement.)

• 0.088

• 0.697

• 0.214

• 0.303

Bob is taking a 100 question test.  They have a 90 % probability of getting any one question correct.  WHICH IS THE CORRECT FORMULA TO FIND OUT THE PROBABILITY that they 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

A test consists of 10 multiple choice questions with five choices for each question. As an experiment, you GUESS on each and every answer without even reading the questions.

What is the probability of getting exactly 6 questions correct on this test?

• (10C6)(1/5)⁶(4/5)⁴

• (10C5)(1/5)⁶(4/5)⁴

• (10C6)(1/5)⁶(4/5)⁵

• (10C5)(1/6)⁵(5/6)⁵

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

• (100C25)(1/6)²⁵(5/6)⁷⁵

• (100C25)(1/6)²⁵(5/6)¹⁰⁰

• (100C4)(1/4)²⁵(3/4)⁷⁵

• (100C4)(1/6)²⁵(5/6)⁷⁵

Suppose that a quiz consists of 20 True-False questions. A student hasn't studied for the exam and will just randomly guesses at all answers (with True and False equally likely). How would you find the probability that the will student get 8 or fewer answers correct?

• Find the probability that X=8 in a binomial distribution with n = 20 and p=0.5.

• Find the area between 0 and 8 in a uniform distribution that goes from 0 to 20.

• Find the probability that X=8 for a normal distribution with mean of 10 and standard deviation of √5

• Find the cumulative probability for 8 in a binomial distribution with n = 20 and p = 0.5.

Leo selects 25 grandparents at random from his town to interview. In the town, 35% of the grandparents have their grandchildren living with them. Let G be the number of grandparents Leo interviews whose grandchildren are living with them. What type of variable is G?

• Geometric

• Binomial

• Both

• Neither

A restaurant offers a game piece with each meal to win coupons for free food. The probability of a game piece winning is 1out of 4 and is independent of other game pieces winning. A family orders 4 meals. Let C be the number of coupons the family wins.

What type of variable is C?

• Geometric

• Binomial

• Both

• Neither

Alma wrote a phone app. She has noticed that 3% of the users who download her app upgrade it the same day. Let N be the number of customers who download Alma's app until one upgrades it on the same day. Assume that the probability of each user's upgrades are independent.What type of variable is N?

• Geometric

• Binomial

• Both

• Neither

The figure shows the probability distribution of a discrete random variable X. Note that the cursor is on the histogram bar representing a value of 6. Which of the following best describes this random variable?

• Binomial with n = 8, p = 0.1

• Binomial with n = 8, p = 0.3

• Binomial with n = 8, p = 0.8

• Geometric with p = 0.2