Name:
Class/Set:
2.5 Theoretical Probability and Relative
Frequency
e-Study Buddy
1
the following events mutually exclusive? Answer ’True’ or ’False’ and give a reason.
1: Are
2
a) Die A lands on a six; die B lands on a four.
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b) A randomly-selected playing card is a Heart; the same card is a red card.
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c) A coin lands Heads up; a coin lands Tails up.
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d) You have a cat; you have a goldfish.
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e) The first ball you pick from a bag is green; the first ball you pick from a bag is red.
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f) A die lands on an even number; a die lands on a prime number.
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g) You are good at Maths; you are good at Science.
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h) It rains today; it is sunny today.
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i) A randomly-selected playing card is a King; the same card is a Queen.
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j) You pass your driving test first time; you fail your first driving test.
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k) Coin A lands Heads up; coin B lands Tails up.
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l) A randomly-selected playing card is a Heart; the same card is a Queen.
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m) A die lands on an even number; a die lands on an odd number.
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1
2: Two
events, A and B, occur with probability p(A) and p(B) respectively.
2
a) If p(A) = 0.07, p(B) = 0.1 and p(A or B) = 0.13, are A and B mutually exclusive?
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b) If p(A) = 0.17, p(B) = 0.42 and p(A or B) = 0.59, are A and B mutually exclusive?
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1
7
c) If p(A) = 23
40, p(B) = 8 and p(A or B) = 10, are A and B mutually exclusive?
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d) If p(A) = 13, p(B) = 16 and p(A or B) = 0, are A and B mutually exclusive?
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e) If p(A) = 0.05, p(B) = 0.08 and p(A or B) = 0.0040, are A and B mutually exclusive?
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f) If p(A) = 0.13, p(B) = 0.07 and p(A or B) = 0.20, are A and B mutually exclusive?
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g) If p(A) = 125 , p(B) = 14 and p(A or B) = 23, are A and B mutually exclusive?
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h) If p(A) = 15, p(B) = 201 and p(A or B) = 0, are A and B mutually exclusive?
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i) If p(A) = 101 , p(B) = 12 and p(A or B) = 35, are A and B mutually exclusive?
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j) If p(A) = 0.04, p(B) = 0.45 and p(A or B) = 0.49, are A and B mutually exclusive?
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k) If p(A) = 0.13, p(B) = 0.44 and p(A or B) = 0.54, are A and B mutually exclusive?
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l) If p(A) = 103 , p(B) = 201 and p(A or B) = 103 , are A and B mutually exclusive?
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m) If p(A) = 0.39, p(B) = 0.11 and p(A or B) = 0.0429, are A and B mutually exclusive?
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Answers: 2.5 Theoretical Probability and
Relative Frequency
e-Study Buddy
1:
1
2
a) False; both events could happen together.
b) False; all Hearts are also red.
c) True; it can’t land with both up at once.
d) False; you could have both.
e) True; it can’t be both colours.
f) False; it could land on 2 (an even prime).
g) False; you can be good at both.
h) False; the weather could change during the day.
i) True; it can’t be both at once.
j) True; you can’t pass and fail the same test.
k) False; both events could happen together.
l) False; it could be the Queen of Hearts.
m) True; it can’t land on both at once.
2:
1
2
a) A and B are not mutually exclusive since 0.13 does not equal 0.07 + 0.1.
b) A and B are mutually exclusive since 0.59 does equal 0.17 + 0.42.
1
c) A and B are mutually exclusive since 107 does equal 23
40 + 8.
d) A and B are not mutually exclusive since 0 does not equal 13 + 16.
e) A and B are not mutually exclusive since 0.0040 does not equal 0.05 + 0.08.
f) A and B are mutually exclusive since 0.20 does equal 0.13 + 0.07.
g) A and B are mutually exclusive since 23 does equal 125 + 14.
h) A and B are not mutually exclusive since 0 does not equal 15 + 201 .
i) A and B are mutually exclusive since 35 does equal 101 + 12.
j) A and B are mutually exclusive since 0.49 does equal 0.04 + 0.45.
k) A and B are not mutually exclusive since 0.54 does not equal 0.13 + 0.44.
l) A and B are not mutually exclusive since 103 does not equal 103 + 201 .
m) A and B are not mutually exclusive since 0.0429 does not equal 0.39 + 0.11.
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