Please show all steps and answers Q2,3 ,4 and 5. Submit solutions to the followi

Question

Please show all steps and answers  Q2,3 ,4 and 5.

Submit solutions to the following problems. 1. P(A) = .36. P(B)=·25, P(A and B) = 0.085. Are events A and B independent? Explain why! 2. P(A)-.3 and P(B)-.6, Find a. P(A or B) when A and B are independent b. P(AlB) when A and B are mutually exclusive. 3. Let die one have sides 0, 3, 3, 3. Let die 2 have sides 2,2,2,5. Let die 3 have sides 1, 1,4, 6 Fine the probabilities that a. die 1 beats die 2 b. die 2 beats die 3 c. die 3 beats die 1 Did something strange occur? 4. In a box are 3 red balls and 5 blue balls. From this box are drawn 4 balls and placed in a second box. Then, one ball is drawn from the second box. What is the probability the ball drawn from the second box is red? 5. Using the same scenario as in the problem above, if we are given the ball drawn from the second box is red, what is the probability that 2 red and 2 blue balls were transferred from box 1 to box 27

Explanation / Answer

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2. P(A) = .4, P(B) = .6

a. If A and B are independent then P(A and B) = P(A)*P(B)
So, P( A or B) = P(A)+P(B) - P(A)*P(B)
= .4+.6-.4*.6
= .76

P(A and B) = .76

b. If A and B are ME then P(A and B) = 0

So, P(A|B) = P(A and B )/P(B) = 0/P(B) = 0

P(A|B) = 0

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