The ten-year survival rate for bladder cancer, when a patient is properly treated, is 55%. If twelve patients who have bladder cancer are properly treated for the disease, what is the probability that: a) less than eleven of them survive past the 10 years? b) What is the expected number of these patients to survive past ten years?

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The ten-year survival rate for bladder cancer, when a patient is properly treated,
is 55%. If twelve patients who have bladder cancer are properly treated for the disease, what is the
probability that:
a) less than eleven of them survive past the 10 years?
b) What is the expected number of these patients to survive past ten years?
Transcribed Image Text:The ten-year survival rate for bladder cancer, when a patient is properly treated, is 55%. If twelve patients who have bladder cancer are properly treated for the disease, what is the probability that: a) less than eleven of them survive past the 10 years? b) What is the expected number of these patients to survive past ten years?
Expert Solution
Step 1

Given:

n = 12

Ten year survival rate =  55%

It means, the probability that the patient survive past ten years is = 0.55

p = 0.55

The probability that the patient did not survive past ten years is = 1-0.55

q = 0.45

Formula Used:

If a random variable X follows Binomial distribution with parameter n and p, then its probability mass function is given by:

P(X = x) = Cxnpxqn-x,        X = 0, 1, 2, 3,.....n

Mean = n×p

 

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