2 A television manufacturer has three locations where it is

2. A television manufacturer has three locations where it is finally assembled. Plants A, B, and C supply 53%, 25%, and 22% respectively of the televisions used by the manufacture. Quality control has determined that 2% produced by Plant A are defective, while 3% from Plant B and 4% from Plant C produce defective products.What is the probability that the television was manufactured by Plant B, given it was not defective?

a. 0.2492
b. 0.2700
c. 0.7850
d. 0.2985
e. 0.5975

3.  At a carnival you win a prize if you get a heads, you must first choose a coin. There is a fair and a biased coin, while choosing each coin is equally likely, the biased coin has a 82% of landing tails. What is the probability of choosing the biased coin if you won a prize.
a. 0.2647
b. 0.3968
c. 0.3421
d. 0.4243
e. 0.3600

Solution

(2) A = 0.53, B = 0.25, C=0.22

Probability of defect for A=0.02, B=0.03, C=0.04

Probability of not being defective for A=0.98, B = 0.97, C=0.96

Probability that a product was manufactured by B given it was not defective = (0.97/0.25)/[(0.98/0.53)+(0.97/0.25)+(0.96/0.22)

= 0.403

(3) Probability of choosing any coin = 0.5

Probab. of getting heads in a fair coin = 0.5

Probab of getting heads in a biased coin = 0.82

So probab that a biased coin was chosen given prize was won = (0.82/0.5)/[(0.82/0.5)+(0.5/0.5)] = 0.621