Statistics question, look at description

Question

At Floyd's Bait Shop and Upstairs University, 90% of freshmen take Statistics. 80% of those who don't take Statistics take Interpretive Dance, while only 50% of those who do take Statistics take Interpretive Dance.

1) What is the probability that a freshman takes Interpretive Dance?

2) What is the probability that a freshman who takes Interpretive Dance doesn't take Statistics?

3) Illustrate this probability model with a tree or Venn diagram.

Answer 1

3.

		Take Interpretive Dance P(D|S)=(.50)
	Take Statistics P(S)=(.90)
		Don’t Take Interpretive Dance P(D’|S)=(.50)
Freshmen
		Take Interpretive Dance P(D|S’)=(.80)
	Don’t Take Statistics P(S’)=(.10)
		Don’t Take Interpretive Dance P(D’|S’)=(.20)

1.The probability that a freshmen takes Interpretive Dance is computed using the Law of Total Probability.

P(D) = P(S)P(D|S) + P(S’)P(D|S’) = (.90)(.50) + (.10)(.80) = .45 + .08 = .53

2. This probability is computed using Bayes Theorem.  

P(S’|D) = P(D|S’)P(S’)/P(D) = .08/.53 = .1509