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

percentage - 25%

probability - 0.25

we know,

total amount of students in class = 20

total boys = 10

total girls = 10

no of girls who wear glasses = 10/2 = 5

probability of choosing a girl with glasses is =

number of girls wearing glasses/total number of students in the class = 5/20

thus, percentage of selecting a girl wearing glasses will be

= 5/20 × 100

= 5 × 5

25%

therefore,

probability will be 0.25

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