Question

The probability that a randomly selected 5-year-old male stink bug will live to be 6 years old is 0.98016.

​(a) What is the probability that two randomly selected 5-year-old male stink bugs will live to be 6 years​ old?

​(Round to five decimal places as​ needed.)

​(b) What is the probability that eight randomly selected 5-year-old males stink bugs will live to be 6 years​ old?

​(Round to five decimal places as​ needed.)

(c) What is the probability that at least one of eight randomly selected 5-year-old male stink bugs will not live to be 6 years​ old? Would it be unusual if at least one of eight randomly selected 5​-year-old male stink bugs did not live to be 6 years​ old? ​(Round to five decimal places as​ needed.)

Answer 1

given that

p = 0.98016

(A)  probability that two randomly selected 5-year-old male stink bugs will live to be 6 years​ old = p^2

setting p = 0.98016

we get

required probability = 0.98016^2

= 0.96071

(B)

probability that 8 randomly selected 5-year-old male stink bugs will live to be 6 years​ old = p^8

setting p = 0.98016

we get

required probability = 0.98016^8

= 0.85187

(C) probability of not living 6 years = 1 - p = 1-0.98016 = 0.01984

using combination, setting n = 8 and r = 0

Probability of at least  one of eight randomly selected 5-year-old male stink bugs will not live to be 6 years​ old is given as

= 1 - C(n,r)*p^r*(1-p)^{n-r}

= 1- C(8,0)*0.01984^0*(1-0.01984)^{8-0}

= 1 - 0.85187

= 0.14813