Question

The probability that machine A will be performing a usual function is 5 years' time is (1/4), while the probability that machine B will still be operating usefully at the end of same period is (1/3). Find the probability that in five years' time a. Both machines will be performing a usual function.

Answer 1

Answer:

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Answer 2

The answer is 1/12

Given:

Let E₁ and E₂ be events defined as:

E₁ the machine A will be performing a usual function

E₂ the machine B will be performing a usual function

P (E₁) = 1/4

P (E₂) = 1/3

To Find:

The probability that in five years

Both machines will be performing a usual function.

Solution:

The events E₁ and are E₂ independent events.

Events Ē1 and Ē2 will also be independent events.

P(both machines will be performing a usual function)

= P (E ∩ F) = P(E) × P (F)

= 1/4 × 1/3

= 1/12

The probability that in five years Both machines will be performing a usual function = 1/12.