1. Probability Conditional Probability
GCSE Statistics
Probability
Conditional Probability

2. When the probability of an event B happening depends on the outcome of a previous event A it is called conditional probability.
We write the probability as P(B|A).
for example, if you take a coloured ball from a bag of mixed colours then take another ball without replacing the first ball, the probability of getting a particular coloured ball depends on what colour the first ball was.
If there were 3 red balls and 7 yellow balls in the bag and Karim chooses a red ball on his first turn then on his second turn the probability of a red ball is (2 red balls left out of 9) and the probability of selecting a yellow ball would be (7 red balls left out of the 9 balls).
If Karim chooses a yellow ball on his first selection then the probability of a yellow ball for his second selection would be and the probability of selecting a red ball on his second try would be 3 9 =
This can be represented on a tree diagram

3. the total of these probabilities is 1Y
3 10
7 10
ball 1
ball 2
3 9
6 9
P(R,R) =
P(R,Y) =
P(Y,R) =
P(Y,Y) =
probability
3 10 × 2 9 = = 1 15
3 10 × 7 9 = 7 30
7 10 × 3 9 = 7 30
7 10 × 6 9 = 7 15
2 9
7 9
the total of these probabilities is 1
The probability of getting two balls the same colour
P(R and R) + P(Y and Y) = = 8 15
the probability of getting a red and a yellow ball would be:
P(R and Y) + P(Y and R) = = 7 15

4. Your turn
Exercise 7K page 283