1. Recap from last lesson
Compliment
Addition rule for probabilities
Mutually exclusive events
Exhaustive events
this is defined as it is certain at least one of the events occur
this is called collectively exhaustive when there are more
than two events

2. Independent events Tree diagrams Conditional probability

3. Starter
A fair six sided die and a coin are thrown together. Find the probability of obtaining a head and a 3 Find the probability of obtaining not a head and not a 3
H H1 H2 H3 H4 H5 H6
T T1 T2 T3 T4 T5 T6

4. Tree diagrams
A fair six sided die and a coin are thrown together Find the probability of obtaining a 3 and a head Find the probability of obtaining not a 3 and not a head

5. Independent events
Independent events are events which have no effect on each other For two independent events A and B P(A and B) = P(A) x P(B) This result is called the multiplication law for independent events

6. For any two independent events
P(B)
P(B’)
P(A)
P(A’)
P(B)
P(B’)

7. Conditional probability
Suppose we think of these playing cards... The probability of someone picking a spade is 1/6 however if we were to know they had picked a black card the probability that they picked a spade would be 1/2. A conditional probability is the probability that an event occurs given that you know another one has happened/is true. The probability that A happens given that B is true is written as P(A|B).

8. The multiplication law of probability
For any two events A and B:
P(B/A)
P(B’/A)
P(A)
P(B/A’)
P(A’)
P(B’/A’)

9. Results relating to conditional probability
P(A and B) P(B)
P(A/B)=
For independent events P(A/B) =
P(A)
This means the first result becomes:
P(A) = P(A and B)/P(B) or rearranged
P(A and B) =P(A) x P(B)

10. A box contains 5 red beads and 3 blue beads.
Two beads are taken out of the bag.
What is the probability of the two beads being the same colour?
What is the probability of the beads being different colours?

11. A bag contains five red and four blue tokens
A bag contains five red and four blue tokens. A token is chosen at random, the colour recorded and the token is not replaced. A second token is chosen and the colour recorded. Find the probability that a the second token is red given the first token is blue, b the second token is blue given the first token is red, c both tokens chosen are blue, d one red token and one blue token are chosen

13. Jean always goes to work by bus or takes a taxi
Jean always goes to work by bus or takes a taxi. If one day she goes to work by bus, the probability she goes to work by taxi the next day is 0.4. If one day she goes to work by taxi, the probability she goes to work by bus the next day is 0.7. Given that Jean takes the bus to work on Monday, find the probability that she takes a taxi to work on Wednesday.