Probability with coin tossing

Question

Toss three coins and let X equal the number of head observed.

A) identify the sample points associated with this experiment and assign a value of X (the number of heads) to each sample point?

B) calculate the distribution function for each value, I.e calculate p(x)?

C) what is the p(X={2,3}), I.e. what is the probability of having at least 2 heads?

Answer 1

HHH

HHT

HTH

HTT

THH

THT

TTH

TTT

p(0 head) = 1/8

p(1 head) = 3/8

p(2 head) = 3/8

p(3 head) = 1/8

P(2 or 3 head) = 3/8+1/8 = 1/2.