A certain federal agency employs three consulting firms (A, B and C) with probabilities 0.40, 0.45 and 0.15. From past experiences, it is known that the probability of cost overruns for the firms are 0.01, 0.14, and 0.17, respectively. Suppose that a cost overrun is experienced by the agency. What is the probability that the firm involved is firm B

68.11% probability that the firm involved is firm B

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Cost overrun

Event B: Agency B used.

A certain federal agency employs three consulting firms (A, B and C) with probabilities 0.40, 0.45 and 0.15.

This means that

From past experiences, it is known that the probability of cost overruns for the firms are 0.01, 0.14, and 0.17, respectively.

This means that

Probability of cost overrun.

Firm A is used 40% of the time, with 1% of these having cost overrun. B is used 45%, with 14% of these having cost overruns. C is used 15% of the time, with 17% of these having cost overruns.

So

What is the probability that the firm involved is firm B

68.11% probability that the firm involved is firm B

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq