Question

A fair coin is tossed 3 times in a row.What is the probability that heads appears exactly 2 time?

Answer 1

First, list all the possible outcomes. You can do this by drawing a tree diagram.

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

There are a total of 8 outcomes.

P(2 heads) = 3/8 = 1/4 = 0.375 = 37.5% (HHT, HTH, THH)
P(at least 2 heads) = P(2 heads) + P(3 heads) = 3/8 + 1/8 = 4/8 = 0.5 = 50%
P(at least 1 head) = P(1H) + P(2H) + P(3H) = 3/8 + 3/8 + 1/8 = 7/8 = 0.875 = 87.5%
P(1 head) = 3/8 = 0.375 = 37.5% (HTT, THT, TTH)
P(1 head on last toss) = 1/8 = 0.125 = 12.5% (TTH)

Answer 2

Easier one:

there are only 8 total outcomes, which might as well be listed !

HHH , HHT , HTH , THH , HTT , THT , TTH , TTT

now count whatever is asked for !

3/8 chance on getting two heads in 3 throws.

Answer 3

remember

t=tails
h=heads