psol06 - Solutions to Homework 6, Math 55 Section 5.1 6....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Solutions to Homework 6, Math 55 Section 5.1 6. There are 4 aces, 13 hearts, and one ace of hearts; thus, by inclusion-exclusion, 4 + 13- 1 = 16 cards are aces or hearts. Therefore, the probability a random card is an ace or a heart is 16 52 = 4 13 . 10. There are ( 52 5 ) total combinations of cards, out of which ( 50 3 ) contain the two of diamonds and the three of spades. Therefore, the probability a hand has these two cards is ( 50 3 ) / ( 52 5 ) = 19600 2598960 = 5 663 . 16. For each suit, there are ( 13 5 ) flushes in that suit, so there are 4 ( 13 5 ) hands which are flushes. Thus, the probability of a flush is 4 ( 13 5 ) / ( 52 5 ) = 5148 2598960 = 13 16660 . 22. Out of the 100 positive integers not exceeding 100, b 100 3 c = 33 are divisible by 3; thus, the probability such an integer is divisible by 3 is 33 100 . 28. There are ( 80 7 ) possible tickets; out of these, ( 11 7 ) are winners. Therefore, the probability of winning is ( 11 7 ) / ( 80 7 ) = 3 / 28879240. Alternately, if we treat the ticket as being fixed, then there are ( 80 11 ) ways for the lottery commissioners to choose the 11 winning numbers. Out of these, there are ( 73 4 ) ways for them to choose your 7 numbers and 4 others. Therefore, the probability of winning is ( 73 4 ) / ( 80 11 ) = 3 / 28879240. 36. When two dice are rolled, there are 5 ways to get a total of 8; thus, the probability of getting 8 is 5 36 . When three dice are rolled, the number of ways to get a total of 8 is the same as the number of solutions to x 1 + x 2 + x 3 = 5, where x i is one less than the number on the i th die. This is ( 5+3- 1 5 ) = ( 7 2 ) = 21, so the probability of getting a total of 8 is 21 6 3 = 7 72 . (Note that since the sum was 5, we didnt have to worry about the fact that each x i 5.) Since 5 36 > 7 72 , getting a total of 8 is more likely with two dice than with three....
View Full Document

Page1 / 3

psol06 - Solutions to Homework 6, Math 55 Section 5.1 6....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online