1. Probability Tree
for
tossing a coin

2. If you toss a coin there are only two ways it can land -or
tails up
heads up
There are two possibilities
½ of the time
the coin will land
½ of the time
the coin will land
heads up
tails up

3. ½ ½ P(H) = ½ P(T) = ½ The probability of a tail, P(T) = ½
a head, P(H) = ½

4. P(H) = ½
P(T) = ½
a second throw can lead to the following outcomes
heads followed by heads
heads followed by tails
tails followed by tails
tails followed by heads

5. ½ ½ ½ ½ ½ ½ P(H,T) = ½ x ½ = ¼ P(T,H) = ½ x ½ = ¼ P(T,T) = ½ x ½ = ¼
P(H,H) = ½ x ½ = ¼

6. ½ ½ ½ ½ ½ ½ P(H,T) = ½ x ½ = ¼ P(T,H) = ½ x ½ = ¼ P(T,T) = ½ x ½ = ¼
P(H,H) = ½ x ½ = ¼

7. What is the probability of getting at least one tail in two tosses?
P(H) = ½
P(T) = ½
P(H,H) = ¼
P(H,T) = ¼
P(T,H) = ¼
P(T,T) = ¼
The probability of getting at least one head in two tosses = P(H,H) + P(H,T) + P(T,H) = ¼ + ¼ + ¼ = ¾
The probability of getting one head and one tail in two tosses = P(H,T) + P(T,H) = ¼ + ¼ = ½
What is the probability of getting at least one tail in two tosses?

8. Complete a probability tree for three tosses of the coin.
P(H) = ½
P(T) = ½
P(H,H) =c ¼
P(H,T) = ¼
P(T,H) = ¼
P(T,T) = ¼
Complete a probability tree for three tosses of the coin.
What is the probability of getting exactly two heads in three tosses?