The probabilities that stock A will rise in price is 0.59 and that stock B will rise in price is 0.41. Further, if stock B rises in price, the probability that stock A will also rise in price is 0.61. a. What is the probability that at least one of the stocks will rise in price? (Round your answer to 2 decimal places.) b. Are events A and B mutually exclusive? c. Are events A and B independent?

a The probability  that at least one of the stocks will rise is 0.75

b The two given events can be seen to be not mutually exclusive

c  The two given events can be seen to be not independent

Step-by-step explanation:

The probability that stock A will rise in price is, p(A) = 0.59

The probability that stock B will rise in price is, p(B) = 0.41

Given that stock B price goes up the stock A price will also go up is,

p(A | B) = 0.61.

a.) Now we know that

      p(A | B)  =     =  0.61 .  

        Therefore = p(B) ×0.61  = 0.41 × 0.61 = 0.25

     the probability that at least one of the stocks will rise

   = p( A ∪ B)

   = p(A) + P(B) -      

    = 0.59 + 041 - 0.25

   = 0.75

b.) For mutually exclusive events we know that p(A | B) = 0 and this is not true in this case as p(A | B) = 0.61

    The two events cannot be said to be  mutually exclusive  

c.)     for independent events

      If the two events have independence then

      p(A|B) =  

Therefore the events A and B are not independent.

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