Question

A bag contains 40 jellybeans with 5 different colors. Each color is equally represented. You are interested in randomly drawing one jellybean at a time and checking the color before eating it. You want to know how many red jelly beans you will pull out of the bag during the first 10 draws. Can the probability be found by using the binomial probability formula? Why or why not?

	No. The trials are fixed, but the events are independent.
	Yes. The trials are fixed and the probability of success remains the same for every trial.
	Yes. The events are dependent; however, the 5% guideline can be applied to this situation.
	No. The events are dependent, and the 5% guideline cannot be applied to this situation.

Answer 1

Solution:

Given: A bag contains 40 jellybeans with 5 different colors. Each color is equally represented.

A jellybean is drawn at a time and checking the color before eating it. So drawing jellybean is without replacement.

x = Number of red jelly beans you will pull out of the bag during the first 10 draws.

when we draw one jellybean and ate it and draw next jellybean, then probability of next draw is not same as before , that is probability of red jellybean is not constant. Hence events are dependent.

Find percent of sample size from population.

Population size = N = 40 and sample size = n = 10

Thus percent of sample size = n / N = 10 / 40 = 0.25 = 25%

Since according to 5% guideline , if sample size is no more than 5% of the population size , then we treat selections as independent.

But here sample size is 25% of the population, so we can not apply 5% guideline.

Thus correct option is fourth option:

No. The events are dependent, and the 5% guideline cannot be applied to this situation.