Question

You are a local startup company working on a smart dashboard camera system. You are bidding to be a supplier for both Ford Motor company and General Motors. Both the companies have a two-tier system where suppliers are approved in two separate phases. A company can move on to Phase II if they have passed the Phase I phase. Historical data points that for a startup company like yours, the chances of landing with a supplier contract with Ford Motor Company is 32% in Phase I while it is 64% in Phase II. However, for General Motors, the chances of success for Phase I is 68% and 36%. Using this information, calculate the following:

(a) What is the probability of your company becoming a successfully approved supplier to Ford Motor Company? Use a tree diagram and standard notations for full credit.(b) What is the probability of your company becoming a successfully approved supplier to General Motors? Use a tree diagram and standard notations for full credit.

Answer 1

(a) The probability of the company becoming a successfully approved supplier to Ford Motor Company is 0.2048.

(b) The probability of the company becoming a successfully approved supplier to General Motors Company is 0.2448.

Explanation:

A local startup company working on a smart dashboard camera system is bidding to be a supplier for both Ford Motor company and General Motors.

Both the companies have a two-tier system where suppliers are approved in two separate phases.

It is provided that a company can move on to Phase II if they have passed the Phase I phase.

(a)

The chances of landing with a supplier contract with Ford Motor Company is 32% in Phase I while it is 64% in Phase II.

That is:

P (Phase I) = 0.32

P (Phase II | Phase I) = 0.64

Consider the tree diagram below.

Compute the probability of the company becoming a successfully approved supplier to Ford Motor Company as follows:

P (Supplier to Ford Motor Company) = P (Phase II | Phase I) × P (Phase I)

`=0.64* 0.32\\=0.2048`

Thus, the probability of the company becoming a successfully approved supplier to Ford Motor Company is 0.2048.

(b)

The chances of landing with a supplier contract with General Motors is 68% for Phase I and 36% for Phase II.

That is:

P (Phase I) = 0.68

P (Phase II | Phase I) = 0.36

Consider the tree diagram below.

Compute the probability of the company becoming a successfully approved supplier to General Motors as follows:

P (Supplier to General Motors Company) = P (Phase II | Phase I) × P (Phase I)

`=0.36* 0.68\\=0.2448`

Thus, the probability of the company becoming a successfully approved supplier to General Motors Company is 0.2448.