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A new surgical procedure is successful with a probability
Chapter 3, Problem 44E(choose chapter or problem)
A new surgical procedure is successful with a probability of \(p\). Assume that the operation is performed five times and the results are independent of one another. What is the probability that
a all five operations are successful if \(p = .8\)?
b exactly four are successful if \(p = .6\)?
c less than two are successful if \(p = .3\)?
Questions & Answers
(2 Reviews)
QUESTION:
A new surgical procedure is successful with a probability of \(p\). Assume that the operation is performed five times and the results are independent of one another. What is the probability that
a all five operations are successful if \(p = .8\)?
b exactly four are successful if \(p = .6\)?
c less than two are successful if \(p = .3\)?
ANSWER:Step 1 of 3
a) We have to find the probability of all operations are successful if \(p=0.8\)
And \(\begin{aligned} \mathrm{q} & =1-0.8 \\ & =0.2 \end{aligned}\)
Given that the operation is performed 5 times
Then \(n=5\)
Let \(X\) be the no.of successful operations
Then \(X \sim B(5,0.8)\)
The pmf of binomial distribution is \(P(x)=n_{C_{x}} p^{x} q^{n-x} ; x=0,1,2,3, \ldots\)
\(\begin{aligned} \mathrm{P}(\text { all operations are successful }) & =\mathrm{P}(\mathrm{X}=5) \\ & =5_{C_{5}}(0.8)^{5}(0.2)^{0} \\ & =0.32768 \end{aligned}\)
Hence the probability of all operations are successful is \(0.32768\)
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Review this written solution for 31495) viewed: 4429 isbn: 9780495110811 | Mathematical Statistics With Applications - 7 Edition - Chapter 3 - Problem 44e
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