Binomial vs Geometric

Describe the process of calculating the probability of a specific number of successes in a binomial distribution.

• Using the square root of the number

• Guessing the probability

• Using the binomial probability formula

• Asking someone else to calculate it

The formula for P(X=k) for a binomial r.v. with number of trials n and a given number of successes k is

• _nC_k

• p^k

• (1-p)^(n-k)

• _nC_k (p)^k (1-p)^(n-k)

The difference between "binomial" and "geometric" distributions is...

• Geometric distributions don't use binary outcome trials.

• Geometric distributions use trials that are not independent.

• Geometric distributions use trials with different success rates.

• Binomial r.v.'s count the number of successes, while geometric r.v.'s count the number of trials until the first success.

X is the number of calls reaching a person that a random-digit dialling machine makes out of 15 attempted calls. The accepted chance of reaching a person through a randomly-dialled call is .12. Which of the following demonstrates the "B" of BINS?

• A set of exactly 15 calls is attempted.

• The call either reaches a person or does not.

• Each call completed doesn't change the odds of reaching the next person.

• A person is reached randomly in 12% of attempts.

Which of these shows the correct formula for finding the probability of getting 2 purple Skittles out of pack of 6, given that the probability of a Skittle being purple is 0.2

• .2²

• .2²*.8⁴

• ₆C₂ = 15

• 15*.2²*.8⁴, or about 24.58%

Compute the probability of getting 1 purple Skittle out of a pack of 6. Again the probability of a given Skittle being purple is .2...

• 8.19%

• 24.58%

• 26.21%

• 39.32%

An opinion poll calls residential telephones at random, with 12% of calls reaching a live person. You watch the poll's random-digit dialling machine make calls and count the number of calls until it reaches a live person, and call that value Y

• Y is geometric, not binomial, because each call's outcome is independent from other calls.

• Y is geometric, not binomial, because each call has the same 12% chance of "succeeding".

• Y is geometric, not binomial, because a call either succeeds or fails.

• Y is geometric, because we count the "trials until a success", not the successes in a fixed number of trials.

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

• geometric

• binomial

• normal

• calculato

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