Question

Suppose you just received a shipment of ten televisions. two 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

Try this solution:

1. for probability of both televisions work:

$P_{2w}=\frac{C^2_8}{C^2_{10}}=\frac{7*8}{9*10}=0.6(2)$

2. for probability of at least on is defective (it means, the sum = one is defective and two are defective):

$P_{1d}=\frac{C^1_2C^1_8}{C^2_{10}}=\frac{4*8}{9*10}=0.3(5)$ - for P(1defective);

$P_{2d}=\frac{C^2_2}{C^2_{10}}=\frac{2}{9*10}=0.0(2)$ - for P(2defective);

totaly for at least one is defective:

$P_{at \ least \ 1 \ d}=P_{1d}+P_{2d}=\frac{16}{45} +\frac{1}{45} =0.3(7)$