Finite Math: Finding Probability & Percentages

Question

Wonder Widgets Inc. has three factories producing the Wham Wonder Widget (WWW). Last year, factory A produced 60 % of all WWW, factory B produced 30% of all WWW, and factory C produced the remaining 10%. Customers have been complaining about their WWW being oversized. The following data was collected.

Factory	% oversized
A	12%
B	7%
C	2%

(a) What % of their total output is oversized?

(b)  If a WWW is oversized, what is the probability that it was produced in factory A?

Answer 1

Let

P(A) = Probability that it is produced by Factory A = 60% = 0.60

P(B) = Probability that it is produced by Factory B = 30% = 0.30

P(C) = Probability that it is produced by Factory C = 10% = 0.10

OS = Oversized

NOS = Not part of the oversized.

What we're looking for are:

(a) P(OS)

(b) P(A | OS)

To solve this, it would be very clear if we have the probability tree first:

___0.12___OS

|

___0.60___ A___|

| |

| |___0.88__NOS

| ___0.07__OS

| |

|___0.30___B___|

| |

| |____0.93__NOS

| ____0.02___OS

| |

|___0.10___C___|

|

|___0.98___NOS

(a) P(OS) = (0.60)(0.12) + (0.30)(0.07) + (0.10)(0.02) = 0.095 = 9.5%

(b) P(A | OS) = P(A  ∩ OS) / P(OS) = (0.60)(0.12)/(0.095) ≈ 0.7579 = 75.79%