Binomial vs Geometric Probability

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

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

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 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.

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

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.

A survey found that 25% of pet owners had their pets bathed professionally rather than do it themselves. If 18 pet owners are randomly selected, find the probability that exactly 5 people have their pets bathed professionally.

• 3.42

• 1.03

• 0.072

• 0.199

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%

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.

Which descriptions are true for a binomial distribution? Select all that apply.

• 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 - success and failure.

• The probabilities must add to 1.

• Each trial must be independent.

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