
Arshiyan K.
asked 07/31/20Which of these random variables has a geometric distribution? HELP ASAP
1.the number of attempts before rolling a 3 with a die
2.the number of defective products in a random sample of 20 taken from a production line that has a 3% defect rate
3.the number of diamonds dealt from a deck of cards
4.the number of 0s produced by a random-number generator
1 Expert Answer

Jon S. answered 07/31/20
Patient and Knowledgeable Math and English Tutor
For a geometric distribution is the probability of the number x Bernoulli trials to get one success or the probability distribution of the number of failures y=x-1 before you get one success.
For a Bernoulli trial, the result is binary (success - get a 3, or failure - not get a 3), each trial is independent (one roll of the die does not affect the next roll), the success rate is constant (1/6 chance of getting a 3 each time) and you cannot get a 3 and not get a 3 on a single roll of the die.
Answer: the number of attempts before rolling a 3 with a die.
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Paige M.
Hi, Arshiyan! Although there is already a response below, I just want to break this down for you in simpler terms in case the other one isn't that clear. For #1, the words "the number of attempts before" are a good indicator of a geometric distribution, since the formal definition of "geometric distribution" is "the number of trials before you get your first ___." For #2, you have a finite number of products in the sample (20). Geometric distributions can only be used for an infinite number of trials. For #3, there are 52 cards in a deck, so since there is a fixed number of trials before obtaining diamonds, this is not indicative of a geometric distribution. #4 is NOT a geometric distribution because it includes EVERY 0 produced by the random number generator, as opposed to the number of trials until you get your FIRST 0 only. I hope this answers your question and clarifies any confusion! So your final answer would be #1 (the number of attempts before rolling a 3 with a die).08/04/20