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12-A-2
Probability
Chapter
12
General probability problems
What to do
1 Two dice are rolled and the difference between the larger and smaller value is recorded.
a List all outcomes using a suitable diagram.
b State the value of n(4).
c Which outcome has the highest probability?
d Which outcome has the lowest probability?
e State P(6).
2
MC Which of the following represents a pair of mutually exclusive events?
A Drawing an ace and a heart with a single draw from a deck of cards
B Having a Year 10 student study Physics and Biology
C Getting an odd number or a multiple of 2 when tossing a single die
D Drawing an ace and a 10 with a pair of cards from a deck
E Staying away from school because of the flu and having a broken arm
3 If P(A) = 0.9, P(B) = 0.3 and P(A ∩ B) = 0.2, P(A ∪ B) = . . . . . . . .
4 If P(A) = 0.8, P(A ∩ B) = 0.4 and P(A ∪ B) = 0.9:
a P(B) = . . . . . . . .
b P(A ∪ B)′ = . . . . . . . .
5 A spinner was spun 1000 times and the following results recorded.
Colour
Red
White
Blue
Green
Yellow
Black
Number
156
144
144
122
89
345
a What is an estimate of P(Black)?
b Are the regions of each colour on the spinner the same area? Justify your answer.
6 A group of 75 students was surveyed to see if they played tennis (T) or golf (G), as shown in the figure
below.
T
G
34 14
12
If a student is chosen at random from this group, calculate:
a P(G)
b P(T′ ∩ G)
c P(T′ ∪ G′)
d Based on this survey, which is the more popular sport? Justify your answer.
7 At lunchtime, 46 people chose soup, while 68 chose the meat dish. Among those, 18 chose both.
If 100 people ate lunch, illustrate this situation with a Venn diagram.
© John Wiley & Sons Australia, Ltd 2012 Maths Quest 10 Individual Pathways Activities
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