Toss a fair coin twice. Find a) sample space, b) P (at least 2 heads), c) the probability distribution?

Answer 1

PROBLEM A:

The sample space is just a listing of all possible outcomes. I'll list them with the first coin and second coin tosses in order:

HH (heads, then heads)
HT (heads, then tails)
TH (tails, then heads)
TT (tails, then tails)

PROBLEM B:

There is only one outcome that has 2 (or more) heads. This is out a 4 possible outcomes, so the probability is 1/4.

PROBLEM C:

P(0 heads) = 1/4
P(1 head) = 1/2
P(2 heads) = 1/4

Answer 2

S={HH, HT, TH, TT}

P(at least 2 Heads) = P(HH) = 1/4

P(HH) = 1/4
P(HT) = 1/4
P(TH) = 1/4
P(TT) = 1/4

P(0 Heads) = P(TT) = 1/4
P(at least 1 head) = P(HT) + P(TH) + P(HH) = 1/4 + 1/4 + 1/4 = 3/4
P(at most 1 head) = P(TH) + P(HT) = 1/4 + 1/4 = 1/2

And it is The Same For The Tails