Before 1918, wolves were shown as 55% male, 45% female. From 1918 to present they were shown as 70% male and 30% female. In a random sample of 12 wolves, what was the probability that 6 were male? What was the probibility that 6 or more were female? What was the probability fewer than 4 were female?

Question

(b) Answer part A for period from 1918 to present

Answer 1

Prob(male) = .7
prob(female) = .3

a) prob(6 are male_
= C(12,6) (.7)^6 (.3)^6 = .07925

b) prob(6 or more are female)
= prob(6 F) + prob(7 F) + prob(8 F + .. prob(12 F_
=
C(12,6)(.3)^6 (.7)^6 + C(12,7) (.3)^7 (.7)^5 + ... + C(12,12) (.3)^12 (.7)^0
I will let you do the button pushing

prob(less than 4 are female)
= prob(3 F) + prob(2 F) + prob (1 F) + prob(0 F)
= C(12,3) (.3)^3 (.7)^9 + ... + C(12, 0) (.3)^0 (.7)^12
= .....