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Statistics Homework Solutions 14

Statistics Homework Solutions 14 - 14 CHAPTER 2 9(a False(b...

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Unformatted text preview: 14 CHAPTER 2 9. (a) False (b) True PJ PA PJ A 06 07 05 ¤ ¡ ¥ ¡ ¤ ¨ ¢¥ ¤ ¨ ¡ ¢ ¡ ¥ PJ A ¥ 11. (a) ¤ ¡ ¨ 08 ¨ ¡ (b) From part (a), the probability that the household gets the rate in at least one month is 0.8. Therefore the probability that the household does not get the rate in either month is 1 0 8 0 2. ¨ ¡ ¨ ¡ (c) We need to find P J Ac . Now P J P J A P J Ac (this can be seen from a Venn diagram). We know that P J 0 6 and P J A 0 5. Therefore P J Ac 0 1. ¥ ¤ ¡ ¨ ¡¥ ¤ ¢¥ ¡ ¤ ¡ ¡¥ ¤ ¥ ¨ ¡¥ ¤ ¡ ¤ ¡ ¨ ¡¥ ¤ 13. (a) Let C be the event that a student gets an A in calculus, and let Ph be the event that a student gets an A in physics. Then ¥ ¡ 0 084 ¨ ¤ 0 146 ¡ ¨ ¢ ¢¥ ¤ ¡ 0 164 0 226 P C Ph ¤ P Ph ¡ PC ¥ ¨ ¥ P C Ph ¤ ¡ ¨ ¡ (b) The probability that the student got an A in both courses is 0.042. Therefore the probability that the student got less than an A in one or both courses is 1 0 042 0 958. ¨ ¡ ¨ ¡ (c) We need to find P C Pc . Now P C know that P C 0 164 and P C P P C P P C Pc (this can be seen from a Venn diagram). We 0 084. Therefore P C Pc 0 08. (d) We need to find P P C c . Now P P know that P P 0 146 and P C P PP C P P C c (this can be seen from a Venn diagram). We 0 084. Therefore P C Pc 0 062. ¡¥ ¢¥ ¤ ¡ ¡ ¡ ¡¥ ¡¥ ¤ ¨ ¥ ¨ ¤ ¡ ¤ ¤ ¤ ¢¥ ¡ ¤ ¨ ¥ ¥ ¡¥ ¡¥ ¤ ¤ ¡ ¤ ¡ ¨ ¥ ¤ ¨ ¡¥ ¨ ¥ ¡ ¡ ¤ ¨ ¢¥ ¢ ¤ ¤ ¡ ¤ ¡ PA B 0 99 ¡ ¡¥ ¤ ¤ ¡ ¨ 0 94 PB 0 95 ¥ PA 0 98 ¡¥ ¨ ¡ ¡ ¥ PA B ¨ ¡ ¤ 15. ...
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