IB Studies

www.ibmaths.com

Adrian Sparrow

Probability 2: constructing tree diagrams

AND and OR 1

A bag contains 3 red counters and 2 blue counters. A counter is picked at random, then replaced in the bag. A counter is then chosen again.

a) Find the probability that 2 red counters are picked.

b) Find the probability that 2 blue counters are picked.

You want: red AND red

Relace the AND with .

P(red) P(red)

=3

5

3

5

9

25

P(blue) P(blue)

=2

5

2

5

4

25

c) Find the probability that the 2 counters are picked are the same colour.

You want:

Red AND red OR blue AND blue

Replace the OR with +.

P(red) P(red) + P(blue) P(blue)

=3

5

3

5

2

5

2

5

13

25

AND and OR 2

A tired maths teacher reaches into her sock draw in the morning. She has 5 black and 3 red socks in the draw. She picks two socks at random.Find the probability that she picks,

a) two black socks,

b) two red socks,

c) matching socks,

d) socks of different colours.

P(black) P(black)=

5

8

4

7

20

56

P(red) P(red)=

3

8

2

7

6

56

5

8

4

7

3

8

2

7

26

56

1

26

56

30

56

Note that this is a question without replacement, so be careful with the second probability.

Tree diagrams - construction

A bag contains 3 red counters and 2 blue counters. A counter is picked at random, then replaced in the bag. A counter is then chosen again.Show this information on a tree diagram.

1st choice 2nd choice

red

blue

red

blue

red

blue

3

5

2

5

3

5

2

5

3

5

2

5

r AND r

9

25

r AND b

6

25

b AND r

6

25

b AND b

4

25

Tree diagrams - reading a table

9

25

6

25

6

25

4

25

Always fill in the probabilities on at the end of the branches, keep the denominators the same and ensure the total is 1.

This makes answering questions much easier.

a) 2 red counters are picked,

b) blue counters are picked,

c) the 2 counters picked are of the same colour,

d) the 2 counters are picked are of different colours.

Find the probability that

9

25

4

25

13

25

12

25

Question

An IB group has 10 males and 10 females. 4 males do SL maths and 6 do HL maths. 7 females do SL and 3 do HL maths. One male and one female are chosen at random and their level of maths is noted.

Male Female

4

10

6

10

7

10

3

10

7

10

3

10

28

100

12

100

42

100

18

100

SL

SL

SLHL

HL

HL

a) Construct a tree diagram for this data.

b) both do HL,

Hence, calculate the probability that when a male and female are chosen at random,

c) both do SL,

d) one does HL,and one does SL.

e) the male does HL, the female does SL.

18

100

28

100

54

100

42

100