In: Statistics and 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)
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 |
1)
total resistor purchases from supplier Y = 500
so probability of randomly selected resistor purchases from supplier Y = 500/1000 = 0.5
2)
number of resistor purchases from supplier X and whcich are faulty = 6
so P( purchases from X and faulty ) = 6/1000 = 0.006
3)
total number of resistor which are faulty = 51
so P( faulty ) = 51/1000 = 0.051
4)
total number of resistors which are not faulty = 949
so, P( not faulty ) = 949/1000 = 0.949
5)
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