1. Give the following table of joint probabilities, please answer the following

Question

1. Give the following table of joint probabilities, please answer the following questions:

(1) According to this table of joint probabilities, please write down the sample space, and identify the events and their outcomes.

(2) Please calculate the marginal probabilities.

(3) Please calculate P(B1|A1), P(B2|A2), and P(B1|A3).

(4) Given A occurred prior to B, and according to your calculations from part (3), please

draw the probability tree.

(5) Please calculate P(A1|B1). Does P(A1|B1) + P(B1|A1) =1 always hold?

(6) Should P(A1|B1) and P(B1|A1) be reciprocals? In other words, did you expect

P(A1|B1) = 1/P(B1|A1) to hold all the time?

(7) Please explain if events A and B are independent or not.

(8) Please calculate P(A1 or B1) and P(A3 or B2).

I know you can only answer a few parts so I'm going to post on another post, please answer the rest for me! If possible answer part 1-3, thanks in andvance!

Explanation / Answer

1) sample space is : { (1,1),(1,2),(1,3),(2,1),(2,2),(2,3)}

here event and outcome are : (A1,B1)=0.1 ; (A1,B2)=0.2 ; (A2,B1)=0.3 ; (A2,B2)=0.1; (A3,B1)=0.2 ;(A3,B2)=0.1

2) from above table:

marginal probability of A is given below:

marginal probability of B is given below:

3)

P(B1|A1)=P(A1 and B1)/PA1) =0.1/0.3 =1/3

P(B2|A2) =P(B2 and A2)/P(A2) =.1/0.4 =1/4

P(B1|A3)=P(B1 and A3)/P(A3) =0.2/0.3 =2/3

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