Answer to Question #150817 in Statistics and Probability for Brittany

Question #150817
Suppose you just received a shipment of 7 televisions. 4 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?

1. The probability that both televisions work is ______
1
Expert's answer
2020-12-15T02:41:50-0500
"P(both \\ work)=\\dfrac{\\dbinom{3}{2}\\dbinom{4}{0}}{\\dbinom{7}{2}}"

"=\\dfrac{\\dfrac{3!}{2!(3-2)!}\\cdot1}{\\dfrac{7!}{2!(7-2)!}}=\\dfrac{3}{21}=\\dfrac{1}{7}"


"P(at\\ least\\ 1 \\ does\\ not\\ work)"

"=1-P(both \\ work)=1-\\dfrac{1}{7}=\\dfrac{6}{7}"



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