Download Level 1 Mathematics, 2009 - SMC-Math

NH 3555
N.C.E.A. LEVEL 1.6
PROBABILITY. 25.
DVD ‘ s.
2 CREDITS.
30 Minutes
You should show ALL working.
1.
Shane sorts his DVDs by the length of movie and by the type of movie as shown in the table.
Less than two hours
Two hours or longer
TOTAL
a)
b)
Comedy
60
64
124
Drama
52
32
84
Thriller
32
69
101
TOTAL
144
161
305
Shane randomly chooses one of the DVDs to watch.
i)
What is the probability that it is a drama.
ii)
Tanya randomly chooses one of Shane’s Comedy DVDs to watch.
What is the probability that the DVD is two hours or longer?
Sarah has sorted her collection of DVDs in the same categories.
78% of her DVDs are less than two hours in length.
Of these,
- 81% are a comedy,
- 9% are a drama,
- the rest are a thriller.
For the DVDs that are two hours or longer,
- 28% of these are a comedy,
- 64% are a drama
- the rest are a thriller.
Some of this information is shown on the tree diagram.
comedy
less than 2 hours
2 hours or longer
c)
i)
Sarah randomly chooses a DVD from her collection.
What is the probability that the DVD she chooses is less than 2 hours and not a thriller?
ii)
5% of Sarah’s DVDs that are less than two hours in length are scratched.
Sarah owns 258 DVDs.
How many of her DVDs that are less than 2 hours in length would you expect to be a
comedy and scratched?
Use probabilities and/or diagrams to explain and support your answer.
2.
a)
Brent has a spinner divided into 4 equal parts, as shown.
Three parts are labelled “3” and one part is labelled “4”.
4 3
3
b)
3
i)
Brent spins this spinner two times.
What is the probability that he spins two 3s?
ii)
What is the probability that when he adds the two numbers he gets together the total is 7?
Brent has another spinner that has four equal parts, as shown.
This spinner has one part labeled “8”, one part labeled “10” and two parts labeled “9”.
4 3
3
3
10 9
8
9
He spins each spinner once, and records the total of the two numbers that the spinners land on.
If Brent spins a 3 on the first spinner what is the probability he records a total of at least 12?
c)
Brent keeps the first spinner that has three parts labelled “3” and one part labelled “4”, and
chooses a six-part spinner that has either a “9” or a “10” on each of its equal parts.
4 3
3
3
? ?
?
?
?
?
He spins both spinners 210 times, and records the total showing each time.
His results are shown in the table.
Total
Frequency
12
26
13
140
14
44
Determine the most likely number of sectors on the second spinner that were labeled with a “9”.
Use probabilities and/or diagrams to explain and support your answer.
NH 3555
Assessment schedule
Determine probabilities
1 ai
aii
bi
bii
2ai
2aii
2b
Explore probabiliy situations Sufficiency
to solve problems
A = 1ai or 1a ii
84
 0.275
305
64
or 0.516
124
Completed tree diagram
accurately with all
probabilities
At least one correct
probability derived
Pr=78% x 81% + 78%
x 9%
= 70.2%
Number < 2 hr = 258 x
0.78
Scratched=
0.05x258x0.78
M = 1b
Scratched comedy =
0.05 x 258 x 0.78 x 0.81
Expect 8 DVDs to be
scratched
Probabilities of each
outcome identified
1
6
as the
probability for a “9”
2A
E = 1bii
A = 2ai or 2a ii
9
or 0.5625
16
6
or 0.375
16
Identifies
2c
Solve probability
problems using
theoretical methods
DVD ‘ s
3
or 0.75
4
3
4
x n6 ≈
M= 2b
26
210
n ≈ 0.9905
1M and 1A or higher
Most likely number of
sectors labelled “9” is one.
1E and 1M or higher
E = 2c