Question

Hey (; I'm taking this rigorous AP Stat course and I've mastered Binomial Sampling but this Geometric Sampling just has me stumped. I actually have a good general idea about how to do each question, but I haven't been able to turn up with the correct answers quite yet. I'd like to compare answers, if you could solve so then I could figure out the process of how to complete the problem, thanks. I'll give best answer btw.

For the scenarios below, determine if the experiment describes a geometric distribution. If it is not a geometric setting, state why. If it is a geometric setting, describe:

1. Roll two six-sided dice and examine their sum. Roll the dice until you roll a sum of 11.

a) the two outcomes
b) what constitutes one trial
c) the probability of success

2. Record the number of made shots a basketball player makes out of 10 attempts.

a) the two outcomes
b) what constitutes one trial
c) the probability of success
3.) There are 5 green marbles and 20 blue marbles in a jar. You reach in and take out a marble. You keep removing marbles until you observe a green marble.

a) the two outcomes
b) what constitutes one trial
c) the probability of success

4.) Draw a card from a standard deck of cards, observe the card, and replace it. Count the number of times you do this until you observe a king

a) the two outcomes
b) what constitutes one trial
c) the probability of success

Answer 1

1) It is geometric

a) In each trial you can obtain 11 or obtain something else (and fail)

b) Throw 2 dices and watch if the result is 11 or not

c) The probability of success is 1/18

2) It is not geometric, but binomal.

Explanation:

1) This is effectively geometric. When you see the sum of 2 dices, you can separate the result in two different outcomes: when the sum is 11 and when the sum is different from 11.

A trial is constituted bu throwing 2 dices and watching if the sum of the dices is 11 or not.

In order to get 11 you need one 5 in one dice and 1 six in another. As a consecuence, you have 2 favourable outcomes (a 5 in the first dice and a 6 in the second one or the other way around). The total amount of outcomes is 6² = 36, and all of them have equal probability. This means that the probability of success is 2/36 = 1/18.

2) This is not geometric distribution. The geometric distribution meassures how many tries do you need for one success. The amount of success in 10 trias follows a binomial distribution.