Question

the probability that a doctor successfully performs an operation is 80%. what is the probabillity that atleast 3 operations out of 4 conducted by him will be successfull??

Answer 1

Answer on Question #49891 - Math - Statistics and Probability

The probability that a doctor successfully performs an operation is 80%. what is the probability that at least 3 operations out of 4 conducted by him will be successful?

Solution.

Let $A = "doctor successfully performs an operation". Then$ P(A) = 0.8 $is probability of success and$ P(\overline{A}) = 1 - P(A) = 1 - 0.8 = 0.2 $ is probability of failure.

Define $ B = "at least 3 operations out of 4 conducted by doctor will be successful"..

Event $B$ consists of two parts. In the first one, 3 operations are successfully performed and one unsuccessful, where unsuccessful operation can be first, second, third or fourth. In the other one, all of 4 conducted operations are successful. In both cases we use binomial distribution.

Thus the probability of $B$ is $P(B) = (0.8)^5(0.2)4 + (0.8)^4 = 0.8192$.

Answer: the probability that at least 3 operations out of 4 conducted by doctor will be successful is 0.8192.

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