Two way tables to calculate conditional probability

Question 1

Example 1 -

Janice asks 100 students if they like biology, chemistry or physics best
38 of the students are girls
21 of these girls like biology best
18 boys like physics best
7 out of 28 students who like chemistry best are gurls

Work out:
P(Boy who likes chemistry best)
P(P|G)
P(Boy|C’)

Answer 1

Bi Ch Ph Total
Boy 28 16 18 62
Girl 21 7 10 38
Total 49 23 28 100

P(Boy likes chemistry best)=16/100
P(P|G)=10/38
P(Boy|C’)=46/77

I got C’ from adding 49 and 28 together, as they are the total of physics and biology, aka all that isn’t the total of chemistry

Question 2

What is the product rule?

Answer 2

The product rule uses multiplication (ANd rule) to calculate the total number of ‘events’

Question 3

Example 2 -

A simple password has a 3 digit combination. The first digit is a number and the second and thirds digits are a letter (lower cased). How many combinations are there?

Answer 3

#     abc  abc
0-9  a-z   a-z
10 x 26 x 26 = 6760

6760 combinations

Question 4

Example 3 -

There are 5 runners in a race. How many different ways could the three medals be allocated?

Answer 4

Gold, silver, bronze
5 x 4 x 3 = 60

Imagine you are choosing the gold position. There are 5 people that could take that gold place. After this position is taken there are only 4 runners left who could take silver. After this position is taken there are only 3 runners who could take gold. Combining all these combinations gives 5 x 4 x 3 possible combinations = 60 combinations.

Question 5

Example 4 -

I want you to choose a pair with one boy and one girl. How many different possibilities are there?
Boys:      Girls:
Adam      Jessica
Joshua    Hannah
Jack         Eleanor
Jacob      Laura
Daniel      Katie
                 Isobel
                 Sasha

Answer 5

Boys: 5
Girls: 7
5 x 7 = 35

Question 6

Example 5 -

There are 16 dogs at Wickersley pet store. Two of the dogs are chosen to compete in Yorkshire’s pet show.
Ali thinks the number of different pairs that can be chosen is 240
Raheem thinks it is 120

Who is correct and why?

Answer 6

Raheem -

16x15=240

16 dogs to choose from at first. Then 15 once the first is picked

Then we need to half it as dog 1 and dog 2 is the same as dog 2 and dog 1. So we get 120, which is Raheem’s answer.