Please show work if needed Thank you The probability that a

Please show work if needed. Thank you!

The probability that a patient recovers from a rare blood disease is 0.4. If 15 people are known to have contracted this disease, what is the probability that at least 10 survive, from 3 to 8 survive, and exactly 5 survive? (Use a Cumulative binomial probabilities table.)

Solution

Answer:

a) 15C10 p^10q^5 + 15C11p^11q^4 + 15c15p^15 , here p = 0.4 and 1 = 1 - p = 0.6

15!/5! x 10! x (0.4)^10 x(0.6)^5 + 15! /4! x 10! x (0.4)^11x (0.6)^4 + 15!/15! x (0.4)^15 = 3003 x 0.00000815372 + 1365 x 0.00000543581 + 0.00000107374 = 3 answer

b) 15Cip^i q^(15-i) , where i ranges from 3 to 8

c) 15C5 = 15! / 10! = 1365