Question

If 15 percent of cars are blue and an observer's observation is 80 percent accurate, what is the probability that a car is, in fact, blue when the witness reports it as blue?

Answer 1

According the question,

15% 0f cars are blue.

∴ P = $\frac{15}{100}$

     = ( .15)

The probability if the car is blue will be ( .15).

An observer's observation is 80 percent accurate.        ( given)

Let us calculate the probability that a car is, in fact, blue when the witness reports it as blue:

⇒ ( .15) ×80%

⇒ $\frac{15}{100}$ ×$\frac{80}{100}$

⇒ $\frac{3}{20}$ × $\frac{4}{5}$

⇒ $\frac{3}{25}$

⇒0.12

Hence the probability that a car is, in fact, blue when the witness reports it as blue is (0.12) or 12%.

Ans :- The probability that a car is, in fact, blue when the witness reports it as blue is (0.12) or 12%.

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