CS 2100: Discrete Structures
Homework 6
CS 2100代写 1.Exercise 3 on page 446. If two dice, one red and one green, are rolled, fifind the probability that (a) Exactly one of the dice is a 6.
1.Exercise 3 on page 446.
If two dice, one red and one green, are rolled, fifind the probability that
(a) Exactly one of the dice is a 6.
(b) The sum of the dice is 5.
(c) The sum of the dice is at least 10.
(d) The value on the red dice is less than the value on the green dice.
(e) The values on the two dice are difffferent.
2.Exercise 9 on page 447. CS 2100代写
A club with 12 female members and 11 male members is forming a budget committee consist-ing of three club members. The club has two offiffifficers: a president and a vice president. How many committees can be formed? Assuming each committee is equally likely to be appointed, fifind that probability that
(a) The committee includes neither the club’s president nor vice president.
(b) The committee has at least one female.
(c) The committee is all-female.
(d) David and Jenny (a married couple) are not both on the committee.
3.Exercise 5 on page 458. CS 2100代写
Two cards are drawn from a deck, with replacement. (This means that one person chooses a card, looks at it , and returns it, and then another person chooses a card, looks at it, and returns it.) Show how to use the product rule to fifind the probability that
(a) The fifirst card is an ace and the second card is black.
(b) Both cards are spades.
(c) Neither card has a value from {2, 3, 4, 5}.
(d) At least one card is an ace. (HINT: Consider the complementary problem.)
4.Exercise 10 on page 459. CS 2100代写
John tosses a penny four times and Jessica tosses a nickel four times. What is the probability that at least one of them gets four results of heads?
5.Exercise 19 on page 465.
Assume that Kenny always gets a hit with probability 1/3 and a base-on-balls with probability 1/6.
(a) Determine the probability that in fifive plate appearances, Kenny gets at least two hits.
(b) Determine the probability that in fifive plate appearances, Kenny gets a base-on-balls at least twice.
(c) Determine the probability that in fifive plate appearances, Kenny gets on base with a hit more times than he gets on with a base-on-balls.
6.Exercise 20 on page 465. CS 2100代写
Suppose the local Barons team wins every game they play with a probability of 0.75. What is the probability that the Barons would win a best-of-seven-game series (i.e., they play games until one team has won four game)? (HINT: Use the results from Example 3 on page 461 and Practice Problem 2 on page 464.)
7.Exercise 4 on page 474.
Suppose a three-person committee is formed for a club by drawing names out of a hat. If the expected number of women on the committee is 2.0 and there are 10 men in the club, how many women are in the club?
8.Exercise 16 on page 474. CS 2100代写
If the Bisons have a 3/5 probability of winning any given game against the Mustangs, what will be the average length of a best-of-fifive series between these two teams?
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