A manufacturer produces soda cans and a quality control worker randomly selects two cans from the assembly line for testing. Past statistics show that 10% of the cans are defective. What is the probability that the two selected cans are defective if the quality control worker selects the two cans from a batch of 40 cans?

P(Both defective) = 1/130

P(Both defective) =23/130

P(Both defective) =1/100

P(Both defective) = 1/5

hayleeirene
Apr 28, 2018

#1**+1 **

Considering each can to be unique, the number of diiferent sets of cans we can form on two successive draws is C(40,2) = 780

And since 10% of the cans are defective......this means that we have 4 defective cans......and we want to choose any 2 of them ....so ..... C(4,2) = 6 possible sets consisting of only defective cans

So....the probability that any set we choose will contain 2 defective cans is :

Sets containing defective cans / Total possible sets =

6 / 780 =

1/ 130

CPhill
Apr 28, 2018