You can purchase a certain type of resistor from supplier X, Y or Z. The probability...

You can purchase a certain type of resistor from supplier X, Y or Z. The probability of having a faulty resistor if the resistor was bought from supplier X is 0.02; from supplier Y is 0.05; and from supplier Z is 0.1. Your company purchased a total of 1000 resistors: 300 from supplier X, 500 from supplier Y, and 200 from supplier Z. Use this information to answer the following questions.

1.What is the probability that a randomly selected resistor was purchased from supplier Y?(round to 3 decimals)

2.What is the probability that a randomly selected resistor was purchased from supplier X and is faulty? (round to 3 decimals)

3.What is the probability that a randomly selected resistor is faulty? (round to 3 decimals)

4.What is the probability that a randomly selected resistor is not faulty? (round to 3 decimals)

5.Given that a randomly selected resistor is faulty, what is the probability that it was purchased from supplier Y? (round to 3 decimals)

Solutions

Expert Solution

solution :

total purchases resistors = 1000

purchases from X = 300

from Y = 500

from z = 200

probabilty of defective from X = 0.02, from Y = 0.05, from z =0.1

first of all preparing an contingency table with the given information

	faulty	not faulty	total
X	300*0.02 = 6	294	300
Y	500*0.05 = 25	475	500
Z	200*0.1 = 20	180	200
total	51	949	1000

total resistor purchases from supplier Y = 500

so probability of randomly selected resistor purchases from supplier Y = 500/1000 = 0.5

number of resistor purchases from supplier X and whcich are faulty = 6

so P( purchases from X and faulty ) = 6/1000 = 0.006

total number of resistor which are faulty = 51

so P( faulty ) = 51/1000 = 0.051

total number of resistors which are not faulty = 949

so, P( not faulty ) = 949/1000 = 0.949

it is given that the selected resistor is faulty we have to find the probabilty that it was purchased from Y

total number of faulty resistors = 51

number of faulty resistors in Y = 25

so P(purchases from Y | it is faulty ) = 25/51 = 0.49

orchestra answered 1 year ago

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