Find the probability

Question

The probability that a patient recovers from a delicate heart operation is 0.9. What is the probability that exactly 2 of the next 4 unrelated patients who have this operation will not recover?

Answer 1

P(R)=.9

P(N)=.1

P(2 of 4 die)=4.86%

P(4 die)=P(0R)= .1^4= .0001

P(4R)=.9^4=.81x.81= .6561

P(2R)=P(2N)=4C2(.1^2)(.9^2)=6x .01x.81=.0486

P(1 dies)=P(3R)=4C3x.1x(.9^3)]=.4x.729= .2916

P(3 die)=P(1R)=4x.9x(.1^3)=.036

P(0)+P(1)+P(2)+P(3)+P(4)=.0001+.036+.0486+.2916+.6561 = 1.000=100%