{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw1sol - UCSD ECE 153 Prof Young-Han Kim Handout#6 Thursday...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
UCSD ECE 153 Handout #6 Prof. Young-Han Kim Thursday, October 9, 2008 Solutions to Homework Set #1 (Prepared by TA Halyun Jeong) 1. Read Sections 2.1 to 2.5 in the text. Try to work on all examples. 2. World Series. The World Series is a seven-game series that terminates as soon as either team wins four games. Suppose San Diego Padres (denoted as A) and New York Yankees (denoted as B) match up in the series. Possible outcomes include AAAA, ABABABA, and BBBAAAA. Assume that each game is independent and both teams are equally strong. (a) Describe the sample space of all possible outcomes. (b) What is the probability that Padres will win the series? (c) What is the probability that all seven games will be played? (d) Suppose Padres lost the first three games. What is the (conditional) probability that they will still win the series? Solution: (a) The sample space consists of two situations: Padres win or Yankees win. First we consider the outcomes that Padres win the game. There are five possible cases. i. Padres don’t lose at all. AAAA There is only one outcome for this case. P { SD 4 - NY 0 } = 1 2 4 = 1 16 ii. Padres lose one game. BAAAA, ABAAA, AABAA, AAABA In this case, there are five games and Padres must win the last game (why), Among first 4 games we can have arbitrary combination of 3A1B, so there are ( 4 1 ) = 4 outcomes. P { SD 4 - NY 1 } = 4 2 5 = 4 32 = 1 8 iii. Padres lose two games. BBAAAA, ABBAAA, AABBAA, AAABBA, BABAAA 1
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
ABABAA, AABABA, BAABAA, ABAABA, BAAABA There are ( 5 2 ) = 10 outcomes for this case. P { SD 4 - NY 2 } = 10 2 6 = 10 64 = 5 32 iv. Padres lose three games. BBBAAAA, ABBBAAA, AABBBAA, AAABBBA, BBABAAA ABBABAA, AABBABA, BABBAAA, ABABBAA, AABABBA BBAABAA, ABBAABA, BBAAABA, BAABBAA, ABAABBA BAAABBA, ABABABA, BABABAA, BAABABA, BABAABA There are ( 6 3 ) = 20 outcomes for this case. P { SD 4 - NY 3 } = 20 2 7 = 20 128 = 5 32 Vice versa, if Yankees win, the cases would be the same. So we can write our sample space as: Ω = AAAA BAAAA, ABAAA, AABAA, AAABA BBAAAA, ABBAAA, AABBAA, AAABBA, BABAAA ABABAA, AABABA, BAABAA, ABAABA, BAAABA BBBAAAA, ABBBAAA, AABBBAA, AAABBBA, BBABAAA ABBABAA, AABBABA, BABBAAA, ABABBAA, AABABBA BBAABAA, ABBAABA, BBAAABA, BAABBAA, ABAABBA BAAABBA, ABABABA, BABABAA, BAABABA, BABAABA BBBB ABBBB, BABBB, BBABB, BBBAB AABBBB, BAABBB, BBAABB, BBBAAB, ABABBB BABABB, BBABAB, ABBABB, BABBAB, ABBBAB AAABBBB, BAAABBB, BBAAABB, BBBAAAB, AABABBB BAABABB, BBAABAB, ABAABBB, BABAABB, BBABAAB
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern