Frequency trees

Question 1

Example 1 -

56 students were asked if they watched tennis yesterday
20 were boys
13 boys didn’t watch tennis
17 girls watched tennis

How many boys watched tennis?

Answer 1

Tennis: 7
Boys: 20
Not T: 13

56

                   Tennis:  17
   Girls: 36
                     Not T: 19

Answer: 7/56 (Do NOT simplify)

Question 2

Example 2 -

30 students were asked if they liked coffee
2/3 of the students were girls
20% of the boys liked coffee
2/5 of the girls didn’t like coffee

How many of the students didn’t like coffee?

Answer 2

Coffee: 2
     Boys: 10      
                    Not C:  8
30
                    Coffee: 12
     Girls: 20 
                    Not C: 8

Answer: 8 boys+8 girls=16 students

Question 3

Example 3 -

There are 4 orange sweets and 5 apple sweets in a bag. Rob takes one out, records its flavor and places it back in the bag. He then takes out a second sweet and records its flavour. Draw a tree diagram to represent this information and calculate the probability Rob:

a. Collects 2 apple sweets
b. Collects an apple and orange sweet
c. Collects at least 1 orange sweet

Answer 3

Orange: 4/9
Orange:4/9
Apple: 5/9

                Apple:5/9   Apple:5/9
                Orange: 4/9

P(OrOr)=4/9x4/9=16/81
P(OrAp)=4/9x5/9=20/81
P(ApAp)=5/9x5/9=25/81
P(ApOr)=5/9x4/9=20/81

a. 25/81
b. P(OrAp)+P(ApOr)=40/81
c. P(OrOr)+P(OrAp)+P(ApOr)=56/81

Question 4

Example 4 -

I have a bag of sweets, 3 red and 7 blue. I pick out two sweets and eat them. Draw a tree diagram to represent the probability I:

a. Pick 2 blue sweets
b. Pick at least 1 red sweet

Answer 4

Red:2/9
Red:3/10
Blue:7/9

           Red:3/9 Blue:7/10
           Blue:6/9

P(RR)=6/90
P(RB)=21/90
P(BR)=21/90
P(BB)=42/90

a. 42/90
b. P(BB)=42/90
90/90-42/90=48/90