Question

Select all situations where a binomial distribution is a reasonable probability model for the random variable X.

A quarter is flipped 3 times to see how many times tails comes up on the coin.

A spinner that has one 10, one 20, one 30, and one 40 is spun 4 times to see how many times a 20 is spun.

A number cube that has 1 on 2 sides, 2 on 2 sides, and 3 on 2 sides is rolled 4 times to see how many times 3 is rolled.

Three marbles are pulled from a bag of 10 green and 10 blue marbles without replacing to see how many times a green marble is pulled.

Answer 1

In many cases, it is appropriate to summarize a group of independent observations by the number of observations in the group that represent one of two outcomes, this means that there are two probably outcome for a problem or situation. Below are the answer to the above question:

1. A quarter is flipped 3 times to see how many times tails comes up on the coin.
2. Three marbles are pulled from a bag of 10 green and 10 blue marbles without replacing to see how many times a green marble is pulled.

Answer 2

A binomial distribution can only be used when there are 2 possible outcomes, no more, no less.

Looking at the situations given you are able to use a binomial distribution in 2 cases.

First is the quarter being flipped 3 times. There are only two possibilities (Heads or Tails).

Second is the 3 marbles being pulled out of the bag. There are only two types of marbles (Green and Blue).