A medicine heals 60% of the patients. 10 sick people get this medicine...

Question

A medicine heals 60% of the patients. 10 sick people get this medicine.



a) What is the probability that all 10 people are cured?

b) What is the probability that at least 1 of the people is cured?

c) What is the probability that exactly 6 people are cured?

Answer 1

X~Bin(n=10, p=0.6)

n = the number of patients

x = the number of patients get the medicine

p = the probability of patients cured

q = the probability of patients not cured

P(X = 10) = [(10!)/(10!)(0!)]*(0.6)¹⁰(0.4)⁰ = (0.6)¹⁰ = 0.0060466176

P(X >= 1) = 1 - P(X = 0) = 1 - [(10!)/(0!)(10!)]*(0.6)⁰(0.4)¹⁰ = 1 - (0.4)¹⁰ = 1 - 0.0001048576 = 0.9998951424

P(X = 6) = [(10!)/(6!)(4!)]*(0.6)⁶(0.4)⁴ = 0.250822656

a) The probability that all 10 people are cured is about 0.006047.

b) The probability that at least 1 of the people is cured is 0.9999.

c) The probability that exactly 6 people are cured is 0.2508.