Probability

Question 1

John rolls two dice and adds their scores. Work out P(12)

Answer 1

1/36

Question 2

John rolls two dice and adds their scores. Work out P(even)

Answer 2

18/36 = 1/2

Question 3

John rolls two dice and adds their scores. Work out p(6)

Answer 3

5/36

Question 4

John rolls two dice and adds their scores. Work out p(odd)

Answer 4

18/36

Question 5

John rolls two dice and adds their scores. Work out p(less than 10)

Answer 5

30/36 = 5/6

Question 6

John rolls two dice and adds their scores. Work out p(prime)

Answer 6

15/36

Question 7

John rolls two dice and adds their scores. Draw a space sample diagram to work out which number would be best to choose, if you’re trying to get that number.

Answer 7

Check blue book, under ‘evaluate’ page. Looks kind of Like one of those multiplication squares.

Question 8

A bag has 7 counters. 3 blue, 4 red. Draw a probability tree diagram for when a counter is taken out, replaced and a counter taken out a second time
b) work out the probability of them being the same colour

Answer 8

Check book for probability tree diagram. Multiply along Brandes, add together when you get more than 1 answer.

4/7x4/7 = 16/49
P(same colour) = 9/49 + 16/49 = 25/49

Question 9

Mary has 4 blue counters and 5 red counters in a bag. She takes two out at random. Find the probability that they are both different colours

Answer 9

Draw a probability tree diagram.
4/9 x 5/9 = 20/72
5/9 x 4/8 = 20/72
20/72 + 20/72 = 40/72 (divide by 8) = 5/9

Question 10

A 6 sided die is rolled 40 times. Here are the results

Score on die | 1 | 2 | 3 | 4 | 5 | 6
Frequency | 10 | 12 | 3 | 8 | 4 | 3

a) what is probability of rolling a 4?
b) what is the relative frequency of rolling a 3?
c) if I rolled the dice 60 times, how many times do you think it would land on a 5?
d) Paul says ‘this is a fair die’; comment on his statement

Answer 10

a) P(4)= 8/40=1/5
b) p(3)=3/40
c) 4/40 of 60= 60/40x4 = 6 times
d) Paul is a liar because I would expect the frequency cause to be the same or at least closer to each other, but they’re not, so I’m calling Paul’s bullshit

Question 11

A factory employs 300 workers. 100 workers are skilled and the rest are unskilled. 25 skilled workers work part time. 130 unskilled workers work full time.

a) draw a frequency tree to show this information
b) how many part time workers are there altogether?
c) if a worker is chosen at random what is the probability that they work full time?

Answer 11

a) check book
b) 25+80=105
c) 75+120/300 = 13/20