Question

Problem 6-27 A project manager is creating the design for a new engine. He judges that there will be a 50-50 chance that it will have high-energy (H) consumption instead of low (L). Historically, 25% of all high-energy engines have been approved (A) with the rest disapproved (D), while 30% of all low-energy engines have been approved. What is the probability that his design will result in an approved engine? Probability=

Answer 1

Probability = 0.275

Explanation:

There are two possible ways for his design to be approved: Being a high-energy engine (H) and being approved or a low-energy energy (L) and being approved.

It is known that there is a 50-50 chance of the engine being high or low-energy.

The probability of approval for each type of engine (E) is given by:

`P(E) = 0.5*A(E)`

Where A(E) is the approval rate for each engine.

Therefore, the probabilities of approval for each type of engine are:

`P(H) = 0.5*0.25\\P(H) =0.125\\P(L) = 0.5*0.30\\P(L) =0.150\\`

The total probability of approval is the sum of both low and high-engine probabilities;

`Probability = P(H)+P(L) =0.125+0.150\\Probability = 0.275`