Mathematics, 17.09.2019 23:00, sunflowerdaisy35
Aboxcar contains six complex electronic systems. two of the six are to be randomly selected for thorough testing and then classified as defective or not defective. (enter your probabilities as )if three of the six systems are actually defective, find the probability that at least one of the two systems tested will be defective. find the probability that both are defective. (b)if four of the six systems are actually defective, find the probability that at least one of the two systems tested will be defective. find the probability that both are defective.
Answers: 2
, where n is the sample size , p is the proportion of getting success in each trial. (1)
![P(x\geq1)=1-P(x=0)\\\\=1-^{2}C_{0}(\dfrac{1}{2})^0(\dfrac{1}{2})^{2} \ \ \text{[By using formula (1)]}\\\\=1-(\dfrac{1}{2})^2\ \ \because\ ^nC_0=1\\\\=1-\dfrac{1}{4}=\dfrac{3}{4}](/tpl/images/0237/7817/1f223.png)
![P(x\geq1)=1-P(x=0)\\\\=1-^{2}C_{0}(\dfrac{2}{3})^0(1-\dfrac{2}{3})^{2} \ \ \text{[By using formula (1)]}\\\\=1-(\dfrac{1}{3})^2\ \ \because\ ^nC_0=1\\\\=1-\dfrac{1}{9}=\dfrac{8}{9}](/tpl/images/0237/7817/61d9f.png)
![P(x=2)=^{2}C_{2}(\dfrac{2}{3})^2(1-\dfrac{2}{3})^{0} \ \ \text{[By using formula (1)]}\\\\=(\dfrac{2}{3})^2\ \ \because\ ^nC_n=1\\\\=\dfrac{4}{9}](/tpl/images/0237/7817/55093.png)
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