a stock will rise .54 and b stock will rise .46...if b rises, the prob of stock a will rise .62

a. find prob at least one will rise

b. are a and b mutually exclusive? yes or no and why (explain plz)

c. are event a and b independent? yes or no and why

P( A rise) = 0.54

P( B rise) = 0.46

P ( A rise | B rise) = 0.62

P( A rise∩ B rise) = P(B rise) P(A rise | B rise) = 0.46*0.62 =0.2852

P ( A rise U B rise) = P( A rise) + P (B rise)- P( A rise∩ B rise)

= 0.54+0.46 -0.2852 = 0.7148

a.

b.

P( A rise∩ B rise) = 0.2852 ≠ 0

A and B are not mutually exclusive

c.

P(A rise) P( B rise) = 0.54*0.46 =0.2484 ≠ 0.2852 = P( A rise∩ B rise)

P(A rise | B rise) =0.62 ≠ 0.54 = P( A rise)

A and B are not independent

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