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answersbookchapter3

# answersbookchapter3 - Chapter 3 1 10 36 P1(366 1 = 1/3 6 9...

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Chapter 3. P1 10 · 1 36 (36 - 6) · 1 36 = 1 / 3 P5 6 2 6 + 9 2 · 9 2 4 + 9 2 = 6 91 P7 For simplicity, do not consider twins. From the four equally likely possibilities (he, sister), (he, brother), (sister, he), (brother, he) (where the elder child is listed first) the last one should not be regarded because the elder brother becomes the king. From the three remaining cases, in two he has a sister. So the answer is 2/3. P8 1/2 P10 13 - 2 52 - 2 . This can be seen directly or from the formula of conditional proba- bility: P (the first is spade | the second and the third are spades) = P ( all three are spades ) P ( the second and the third are spades ) = 13 3 / 52 3 13 2 / 52 2 = 11 50 P17 (a) P ( DC ) = P ( D ) · P ( C | D ) = . 36 · . 22 = . 0792 (b) P ( D | C ) = P ( DC ) P ( C ) = . 0792 . 3 = . 264 P18 (d) P ( V ) = P ( V I ) + P ( V L ) + P ( V C ) = P ( I ) · P ( V | I ) + P ( L ) · P ( V | L ) + P ( C ) · P ( V | C ) = . 46 · . 35 + . 30 · . 62 + . 24 · . 48 = . 4862 (or 48.62%) (a) P ( I | V ) = P ( IV ) P ( V ) = P ( I ) · P ( V | I ) P ( V ) = . 46 · . 35 . 4862 = . 331 ...

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