Conditional Probability and Tree Diagrams Ex 5E Q 3, 4

1
Conditional Probability and Tree Diagrams Ex 5E Q
3, 4 5
2
B
0.6 x 0.6 0.36
0.6
B
0.6
0.6 x 0.4 0.24
T
0.4
Bus
0.7
B
0.4 x 0.7 0.28
0.4
Taxi on Wed 0.24 0.12 0.36
T
0.3
T
0.4 x 0.3 0.12
3
H
0.5 x 0.5 0.25
0.5
F
0.5
0.5
0.5 x 0.5 0.25
T
0.5
1
F
0.5 x 1 0.5
T

• P(Heads) 0.25
• P(F O T) P(FT) x P(T) ? 0.25 P(FT) x 0.75
• ? P(FT) 0.25 0.75 ? P(FT) 0.333

4
F
3/4 x 1/3 1/4
1/3
T
3/4
3/4 x 2/3 1/2
2/3
F
1/4
1
H
1/4 x 1 1/4
F
5
1
Win
1/3
R
T
1/3
1
1/3
1/3
T
R
1/3
1
1/3
R
T
6
A contestant has two darts and wins a game if
he/she can bursts a balloon using these two
darts. The probability of a burst with the first
attempt is 1/3. If the contestant fails with the
first attempt, the second attempt has a
probability of 1/2. What is the probability of
bursting the balloon?
7
B
2/3 x 1/2 1/3
1/2
1/2
2/3 x 1/2 1/3
B
2/3
B
1/3
B
1/3
2/3
A contestant has two darts and wins a game if
he/she can bursts a balloon using these two
darts. The probability of a burst with the first
attempt is 1/3 and if the contestant fails with
the first attempt the second attempt has a
probability of 1/2. What is the probability of
bursting the balloon?