Is there anyone that can help me with this question? Still not figure out step b

Question

Is there anyone that can help me with this question?

Still not figure out

step by step explanations please :(

8. Recall the M&M;/Bayes' Rule experiment from class. We will modify the experiment slightly here. Here is the setup: There are two cups, A B. A contains 40 and 10 Green. Cup B contains 10 Green M&Ms; and 40 There is no way to tell from the outside which cup is which. One of the cups is randomly chosen and set aside (call this the Chosen Cup). The other cup gets thrown into a wood chipper and destroyed unseen. The identity of the Chosen Cup is a mystery, but of course the initial probability that it is Cup A is 50. a. (0 points) An M&M; is randomly picked from the Chosen Cup. It is Red. What is the probability that the Chosen Cup is Cup A? ea A EXTRA CREDIT (10 points) b. The M&M; from part a is returned to the chosen cup. We reach back into the cup and randomly select M&M.; It Red. What is the probability that the Chosen is

Explanation / Answer

Since both cups are equally likley so

P(A) = P(B) = 0.50

(a)

Let R shows the event that Red M&M is choosen.

There are 50 M&M in the cup A out of which 40 are red so

P(R|A) = 40/50

and there are 50 M&M in the cup B out of which 40 are red so

P(R|B) = 40/50

Now by the law of total probability, we have

P(R) = P(R|A)P(A)+P(R|B)P(B)=(40/50)*0.50+(40/50)*0.50=0.8

SO the probability that choosen cup is cup A, by the Baye's theorem is

P(A|R) = [P(R|A)P(A)] / P(R) = [(40/50) * 0.50] / 0.8 = 0.50

(b)

Same as part A because M&M returned to same cup.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.