MS-Sol-EE-C13

MS-Sol-EE-C13 - CHAPTER 13 PROBABILITY PROBABILITIES OF...

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CHAPTER 13 PROBABILITY: PROBABILITIES OF COMPOUND EVENTS EXERCISE 13.1 Section 13.1 The addition rule (page 221) 1. (a) The outcomes that give a total of 7 are: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1). P(total = 7) = 6 36 = 1 6 (b) The outcomes that give a total of 10 are: (4, 6), (5, 5), (6, 4). P(total = 10) = 3 36 = 1 12 (c) P(total = 7 or 10) = P(total = 7) + P(total = 10) = 1 6 + 1 12 = 1 4 2. (a) P(2 or 4 machines sold) = 0.25 + 0.10 = 0.35 (b) P(more than 3 machines sold) = P(4 or 5 machines sold) = 0.10 + 0.05 = 0.15 (c) P(at least 1 machine sold) = 1 – P(none sold) = 1 – 0.15 = 0.85 3. (a) P(failing within 2 years) = 0.43 + 0.32 = 0.75 (b) P(surviving at least 3 years) = 0.09 + 0.05 = 0.14 4. (a) P(not more than 1 defective) = P(0 defective) + P(1 defective) = 0.73 + 0.18 = 0.91 (b) P(more than 1 defective) = 1 – P(not more than 1 defective) = 1 – 0.91 = 0.09 120
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C HAPTER 13 P ROBABILITY : P ROBABILITIES OF C OMPOUND E VENTS 5. (a) P(a Chinese) = 0.10 + 0.23 + 0.02 = 0.35 (b) P(an American) = 0.13 + 0.25 = 0.38 (c) P(a Chinese or an American) = 0.35 + 0.38 = 0.73 6. (a) P(the customer is a resident or pays by cash) = 36 + 124 + 60 36 + 124 + 60 + 20 = 220 240 = 11 12 (b) P(the customer pays by credit card or is a non-resident) = 124 + 20 + 60 240 = 204 240 = 17 20 7. Scenery Portrait Still Image Total Jenny 19 33 28 80 Terry 43 32 25 100 Total 62 65 53 180 (a) P(photo is taken by Jenny) = 180 80 = 9 4 (b) P(photo is a portrait or taken by Terry) = P(photo is a portrait) + P(photo is taken by Terry) – P(photo is a portrait and taken by Terry) General addition rule = 180 32 180 100 180 65 - + = 180 133 8. (a) The required probability = 10 + 35 500 = 9 100 (b) The required probability = 35 + 75 + 70 + 52 + 83 = 63 100 500 (c) The required probability = 70 + 35 + 10 + 75 + 83 + 82 = 71 100 500 121
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S ECTION 13.1 T HE A DDITION R ULE 9. (a) P(heart) = 52 13 = 4 1 (b) P(king) = 52 4 = 13 1 (c) P(heart or king) = P(heart) + P(king) + P(heart king) = 52 1 13 1 4 1 - + = 13 4 10. (a) P(divisible by 3) = 10 30 = 1 3 (b) P(divisible by 5) = 6 30 = 1 5 (c) P(divisible by 3 and 5) = P(divisible by 15) = 2 30 = 1 15 P(divisible by 3 or 5) = P(divisible by 3) + P(divisible by 5) - P(divisible by 3 and 5) = 1 3 + 1 5 1 15 - = 7 15 11. (a) Q A and B are mutually exclusive. P( A B ) = 0 P( A B ) = P( A ) + P( B ) - P( A B ) = 0.2 + 0.7 - 0 = 0.9 (b) P( A ) = 1 - P( A ) = 1 - 0.2 = 0.8 (c) P( A B ) = P( B ) = 0.7 12. (a) P( A ) = P[ A ( B B )] ( Q B B = universal set) = P[( A B ) ( A B )] (distributive law) = P( A B ) + P( A B ) (addition law) = 0.3 + 0.4 = 0.7 (b) (i) P( A B ) = P( A ) + P( B ) - P( A B ) = 0.7 + 0.45 - 0.3 = 0.85 (ii) B = ( A B ) ( A B ) P( B ) = P( A B ) + P( A B ) P( A B ) = 0.45 - 0.3 = 0.15 122
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C HAPTER 13 P ROBABILITY : P ROBABILITIES OF C OMPOUND E VENTS 13. If A B , then B = A ( B
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MS-Sol-EE-C13 - CHAPTER 13 PROBABILITY PROBABILITIES OF...

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