SOLUTION: The probability that a particular surgery is successful is 0.70. Find the probability that none of the four such surgeries is successful: (choose 2) 0.81% 3/7 The events are

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Question 938756: The probability that a particular surgery is successful is 0.70. Find the probability that none of the four such surgeries is successful: (choose 2)
0.81%
3/7
The events are independent from each other.
0.3
The events are dependent on each other.
Answer by mathmate(429) About Me  (Show Source):
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First we have to establish independence.
Most of the time, the surgeries are on separate and unrelated patients, and they are not normally done by the same surgeon. So it is a reasonable assumption that individual surgeries are independent. Besides, there is no information on dependence, if any.
We conclude that "The events are independent from each other." is one of the choices.

Now to find the probability, we are given that
P(success) = p = 0.70
which leads to
P(failure) = q = 1-p = 1-0.70 = 0.30

Using the multiplication rule, which says that the probability of multi-step events which are independent is the product of the individual probabilities.

P(4 failures) = q%5E4 = +0.3%5E4+ = 0.0081 = 0.81%

Answer: probability of 4 unsuccessful surgeries is 0.81%