Geometric and Binomial Distributions

If we want to calculate the probability of rolling a 6 for the first time on the 6^th roll of a die, would we use the geometric or the binomial distribution?

• geometric

• binomial

Which of the following is false about binomial probabilities?

• Their distributions are approximately symmetric.

• Trials must be fixed.

• Events musts be independent.

• The probability of success must be 0.50

When rolling a fair die 100 times, what is the probability of rolling a "4" exactly 25 times? Is this an example of binomial or geometric?

• binomial

• geometric

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

If you want to know how many trials you will need before your first success, use the ????? model.

• Geometric

• Binomial

• Normal

• Calculator

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.

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

• geometric

• binomial

• normal

• calculato

The owner of a pet store is trying to decide whether to discontinue selling specialty clothes for pets. She suspects that only 4% of the customers buy specialty clothes for their pets. What is the probability that she does NOT sell a garment until the 7th customer? Assume each customer is independent.

• 0.033

• 0.027

• 0.0313

• Not here

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