Download Worksheet 11.2

Maths Quest Maths B Year 11 for Queensland
Chapter 11 Introduction to probability WorkSHEET 11.2
1
WorkSHEET 11.2 Introduction to probability Name: ___________________________
1
Jason is a goalkicker in a Rugby League team.
186
Relative frequency =
During the season he kicked 186 goals from
250
250 attempts. Find the relative frequency of his
= 0.744
successfully kicking a goal.
2
2
A car manufacturer sells 32 000 cars over a
1500
Relative
frequency
=
 100%
period of 1 year. Each car has a one year
32000
warranty and 1500 of the cars sold need to have
= 4.6875%
repairs done under warranty. As a percentage,
find the relative frequency of a car needing
repairs under warranty.
2
3
A manufacturer of a video recorder keeps track Total number of video recorders = 300
2
of the age of recorders that are in need of
Number needing repair in warranty period = 32
repair.
Age (months) No. of videos
32
Percentage needing repair =
 100%
0-3
2
300
3-6
6
= 10.7%
6 - 12
12 - 24
24 - 36
over 36
24
45
125
98
The manufacturing process will need to be
upgraded.
The manufacturer of the video recorders offers
a 12-month warranty. If more than 10% of
videos require repairs in the warranty period,
the manufacturing process will need to be
upgraded. Determine if this will be necessary.
4
Generate a series of 10 random numbers
between 1 and 100.
Answers vary
2
5
(a)
Generate a series of random numbers to
simulate 60 rolls of a die.
Answers vary
4
(b)
Draw a frequency histogram of your
results.
Maths Quest Maths B Year 11 for Queensland
6
Chapter 11 Introduction to probability WorkSHEET 11.2
Consider this table of calculator-generated
random numbers. Use them to simulate the
tossing of a coin and list the outcomes.
0.231
0.593
0.362
0.863
2
0 to 0.500 represents tail (T)
1
0.501 to 1.000 represents head (H)
T, T, T, H, H, H, H, H, T, T
0.142 0.652 0.811
0.921 0.398 0.021
7
Given this sequence of 18 coin tosses,
determine its long-run proportion for Tails.
H, H, T, H, T, T, H, T, T, T, H, T, H, T,T,T,H,
T, T, H.
8
A die which is suspected of being biased,
250
(unfair) is tossed 900 times and it was observed Long-run proportion = 900
that a ‘5’ appeared 250 times. Calculate the
= 0.278
long-run proportion and comment, based on the
1
expected proportion.
Expected proportion =
6
= 0.167
1
12
20
= 0.6
Long-run proportion of Tails =
2
The long-run proportion is not about equal to
the expected proportion. Hence, the die is
biased.
9
A travelling saleswoman records her daily
success rate at selling carry-bags. Compute her
long-run proportion of sales to houses visited
for each day and comment on whether she is
improving her ability as a saleswoman.
Sales
5
Houses visited 22
10
2
20
10
30
8
25
12 15
24 25
14
20
Three trainee bakers record the number of
loaves of bread sold and the number ordered
for a month. Work out the proportions to find
which baker is the most effective.
Baker
Loaves sold
Loaves ordered
1
60
90
2
150
198
3
260
300
2
Sales
5
2 10 8 12 15
Houses visited 22 20 30 25 24 25
Proportion
0.23 0.1 0.3 0.3 0.5 0.6
The proportion of sales is increasing; thus, the
saleswoman’s ability is improving.
2
Baker
Loaves sold
Loaves ordered
Proportion
1
60
90
0.67
2
150
198
0.76
3
260
300
0.87
Baker 3 has the greatest proportion, 0.87, and
hence is the most effective.