The probabilities that stock A will rise in price is 0.47 and that stock B will rise in price is 0.53. Further, if stock B rises in price, the probability that stock A will also rise in price is 0.57. 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? Yes because P(A | B) = P(A). Yes because P(A ∩ B) = 0. No because P(A | B) ≠ P(A). No because P(A ∩ B) ≠ 0. c. Are events A and B independent? Yes because P(A | B) = P(A). Yes because P(A ∩ B) = 0. No because P(A | B) ≠ P(A). No because P(A ∩ B) ≠ 0.

Step-by-step explanation:

P(A) = 0.47

P(B) = 0.53

P(A|B) = 0.57

a. Probability that at least one stock will rise is equal to P(A u B)

= P(A) + p(B) - P(A n B)

= (O.47+0.53)-(0.53*0.57)

= 1-0.3021

= 0.6979

b. Events A and B are not mutually exclusive. This is because P(AnB)≠0

P(AnB) = p(B).P(A|B)

= 0.53x0.57

= 0.3021 and this value is not equal to 0

c. No, events A and B are not independent. This is because P(A|B) ≠ P(A)

Since we have

p(A) as 0.47

P(A|B) as 0.53

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.

goog may have it for you