(Spts each) A box has 7 red balls and 3 blue balls. Two balls are drawn at rando

Question

(Spts each) A box has 7 red balls and 3 blue balls. Two balls are drawn at randonm without replacement. That is, a ball is drawn at random, and without putting the first ball back into the box, a second ball is drawn at random. Define the events A and B as follows: A: The first ball is red. B: The second ball is blue. 3 . (a) True or false, P(B)-3/9. If false, what is this probability? If true, no justification is needed, though partial credit may be given if justifica- tion is given and the answer is wrong. (b) True or false, P(BIA) 3/9. If false, what is this probability? If true, no justification is needed, though partial credit may be given if justifica- tion is given and the answer is wrong. (c) Find P(AUB). --(d) Are events A and B disjoint, independent, both, or neither? Give justification for your answer (Here, at random means that each possible option is selected with equal probability)

Explanation / Answer

A) P(A) = 7/10

P(B) = P(first ball is red and second is blue) + P(first is blue and second is blue)

= 7/10 * 3/9 + 3/10 * 2/9

= 3/10

So, False.

B) P(B | A) = P(B and A) / P(A) = (7/10 * 3/9) / (7/10) = 3/9

So, true.

C) P(A U B) = P(A) + P(B) - P(A And B)

= 7/10 + 3/10 - 7/10 * 3/9

= 23/30

D) since P(B | A) is not equal to P(B), A and B are not independent.

Since, P(A and B) is not zero, they are not disjoint.

So option is neither.

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