Solve for x ? Help me please

0.4138 or 41.38%

Step-by-step explanation:

Prob(a) = 0.15

Prob(b|a) = 0.80

A = event that taxi is blue

B = witness says it is blue

Prob(taxi is not blue) = 1 - prob(a)

= 1- 0.15

= 0.85

Prob(b|a') = 1 - prob(b|a)

= 1 - 0.8

= 0.20

Using addition rule

P(b) = p(a)p(b|a) + p(a')p(b|a')

= 0.15 * 0.8 + 0.85 * 0.20

= 0.29

Now we are to find probability that the taxi that is at fault is blue

According to bayes theorem

P(a|b) = P(a)*p(b|a) / p(b)

= 0.15 x 0.8 / 0.29

= 0.4138