Question

In a workplace, three robots, Q, R and S, are employed to make chairs.

Robot Q makes 25% of the chairs
Robot R makes 45% of the chairs
The remaining chairs are made by Robot S

Evidence has shown that 2 percent of the chairs made by robot Q are defectives, 3 percent of the chairs made by robot R, and 5 percent of the chairs made by robot S are defective.

a. Construct a tree diagram that illustrates all possible outcomes and probabilities.

A chair is randomly selected.

b. What is the probability that the chair that robot Q made is defective.

c. What is the probability of findings a broken chair.

d. Given that a chair is defective, what is the probability that it was not made by robot R.

Answer 1

Answer:

Three percent of chair was not made by robot r

Answer 2

Given: Robot Q makes 25% of the chairs. Robot R makes 45% of the chairs. The remaining chairs are made by Robot S. Evidence has shown that 2 percent of the chairs made by robot Q are defectives, 3 percent of the chairs made by robot R, and 5 percent of the chairs made by robot S are defective.

To find:  a.  chair is randomly selected.

b. What is the probability that the chair that robot Q made is defective.

c. What is the probability of findings a broken chair.

d. Given that a chair is defective, what is the probability that it was not made by robot R.

Solution:

Q makes 25% of chairs and R makes 45% of chairs. This means the remaining 30% of chairs are made by S.

Q makes 2% of chairs defective out of 25&%.

R makes 3% defective out of 45%.

S makes 5% defective out of 30%.

The probability that the chair made by Q is randomly selected= 25/100 = 1/4

The probability that the chair made by R is randomly selected= 45/100= 9/20

The probability that the chair made by S is randomly selected= 30/100= 3/10

the probability that the chair that robot Q made is defective= 2/25

the probability of findings a broken chair= 2+3+5/ 100= 1/10

Given that a chair is defective,  the probability that it was not made by robot R= PROBABILITY THAT IS MADE BY Q OR S

= 2/25+5/30= 12+25/150= 37/150

A chair is randomly selected= 1/4, 9/20, 3/10

b. What is the probability that the chair that robot Q made is defective= 2/25

c. What is the probability of findings a broken chair= 1/10

d. Given that a chair is defective,the probability that it was not made by robot R= 37/150