Question

A manufacturer of tablets receives its LED screens from three different suppliers, 45% from supplier B1, 30% from supplier B2, and the rest from supplier B3. In other words, the probabilities that any one LED screens received by the plant comes from Bis 0.45 and from B2 is 0.30. Also, suppose that 95% of the LED screens from B1, 80% of those from B2, and 65% of those from B3 perform according to specifications. Find the:

a) Find the probability that a LED screen will meet specifications.
b) Calculate the probability that a LED screen that meets specifications was sent by the second supplier.

Answer 1

a) 0.83 = 83% probability that a LED screen will meet specifications.

b) 0.2892 = 28.92% probability that a LED screen that meets specifications was sent by the second supplier.

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

45% from supplier B1, 30% from supplier B2, and the rest from supplier B3.

So 100 - (45 + 30) = 100 - 75 = 25% from supplier B3.

a) Find the probability that a LED screen will meet specifications.

95% of 45%(supplier B1)

80% of 30%(supplier B2)

65% of 25%(supplier B3). So

`p = 0.95*0.45 + 0.8*0.3 + 0.65*0.25 = 0.83`

0.83 = 83% probability that a LED screen will meet specifications.

b) Calculate the probability that a LED screen that meets specifications was sent by the second supplier.

Conditional probability.

Event A: Meets specifications.

Event B: Sent by second supplier.

0.83 = 83% probability that a LED screen will meet specifications.

This means that
`P(A) = 0.83`

Meets specifications and is sent by the second supplier.

80% of 30%, so

`P(A \cap B) = 0.8*0.3 = 0.24`

Probability:

`P(B|A) = (P(A \cap B))/(P(A)) = (0.24)/(0.83) = 0.2892`

0.2892 = 28.92% probability that a LED screen that meets specifications was sent by the second supplier.