Calculate the probability that a mortgage is an adjustable r

Calculate the probability that a mortgage is an adjustable rate given that is it for a single-family property. What is the probability the mortgage is fixed? What is the probability it is for a single family? Are the events \"the mortgage is fixed\" and \"the mortgage is for a single family\" independent?

Solution

(a)

P(adjustable and single-family) = 0.4

P(single-family) = 0.5

So required conditional probability is

P(adjustable | single-family) = P(adjustable and single-family) / P(single-family) = 0.4 / 0.5 = 0.8

(b)

From table

P(fixed) = 0.3

(c)

From table

P(single-family) = 0.5

(d)

P(fixed and single-family) = 0.1

P(fixed)*P(single-family) = 0.3*0.5 = 0.15

since P(fixed and single-family) is not equal to P(fixed)*P(single-family) so they are not independent.