3 coins are flipped, find the probabilities of:

Question

a) P(two heads)
b) P(at most two heads)
c) P(no heads)

Answer 1

I will do one b)

Pr(at most two heads)=1-Pr(three heads)-Pr(no heads)

Pr(at most two heads)=1-(1/2)^3 - (1/2)^3
= 1-2/8= .75

Lets do it the other way..
Pr(at most two heads)=Pr(one head) + Pr(two heads) Now note, there are three ways one can get one head, and three ways one can get two heads.
= 1/2*1/2*1/2 *3 + 1/2*1/2*1/2*3=.75