Question

Suppose you just received a shipment of thirteenthirteen televisions. ThreeThree of the televisions are defective. If two televisions are randomly​ selected, compute the probability that both televisions work. What is the probability at least one of the two televisions does not​ work?

Answer 1

Here there are thirteen televisions. Three of the televisions are defective that means 10 are non defective

if two televisions are randomly selected.

Total combinations to select two televisons out of 13 = ¹³C₂ = 78

Here we have to find  the probability that both televisions work,

so here the total arrangements that the two selected televisiosn are from non defective = ¹⁰C₂ = 45

Pr(Both televisions work) = 45/78 = 15/26

Now at least one of two television doesnot work that means either one or both television doesnot work that means

Pr(BOth televisions work) = 1 - Pr(at least one of the television doesn't work) = 1 - 45/78 = 1 - 15/26 = 11/26