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Take a Test-Mark Dover-Goegle Chrome . Secure | https//www.mathalcom/Student/PlayerTestaspxhestide175367258&centerwinyes; Math 224 Intro to Probability and Statistics Spring 2018 Mark Dover | 2/28/18 12:47 Quiz: Quiz2Online Time Remaining: o00 28 04 Submit This Question: 1 pt 14 of 15 (7 complete) This Quiz: 15 pts po Suppose that A and B are two events a. What does it mean for event B to be independent of event A? b. it event A and event B are independent. how can their joint probability be obtained from their marginal probabilities? a·Choose the correct answer below O A. Event B is said to be independent of event A iHPIA & B) PIA or B) OB. Event B is said to be independent of event AIP(A & B)-o OC. Event B is said to be independent of event AyPiBIA)·PB) OD. Event B is said to be independent of event A#AA or B)-1 b. Choose the correct answer below A. The joint probablity equals the sum of the marginal probabines mna the probabaty that ether event wd occur that is PA & B) a PA) + PiB) O B. The jont probablit, equals the sum of magnal probablbes that is. P(A & B) P18) C. The joint probablity equals the peoduct of the mwghal probablies that is p(A & B-RA). PB) D. Thejoint probablity equals the product of the marginal probablities minun. sum of the margral probabilses thatis P(A & B-PA,He-RIA)· Cick to s Recent Achievements

Explanation / Answer

A and B are two events.

a. If A and B are independent, then P(A|B) = P(A).

Also, P(B|A) = P(A).

The correct answer is:

C.

b. We have P(A|B) = P(A and B) / P(B) by Baye's theorem.

Since A and B are independent, P(A|B) = P(A)

=> P(A) = P(A and B) / P(B)

=> P(A and B) = P(A) P(B).

Therefore, the correct answer is :

C.

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