1. (a) If W = the set of all days of the week, and Y is the set of all words or
ID: 3304833 • Letter: 1
Question
1.
(a) If W = the set of all days of the week, and Y is the set of all words or names that end in
the letter y, how many elements are in the intersection of W and Y?
(b) If B = the set of all birds currently swimming in the lake, and D = the set of all Ducks that are members of B, describe the set that is the complement of D in B.
(c) If you draw 3 cards without looking at it from a standard 52-card deck designed for playing poker, what is the probability that all three cards will be Aces?
(d) If you roll a standard six-sided die, what is the expectation of the number of dots on the top of the die?
(e) In September in New York, the high temperature exceeded 80°F on 18 days. It rained on 3 days when the high temperature was over 80°F. If we choose any day in September, the probability that it rained on that day is independent of the probability that the high temperature was over 80°F. Therefore, how many days did it rain in September?
(f) Hex Yahtzee is a game in which each person rolls six dice at once. The dice are ordinary 6-sided cubes, with a different number on each face. If exactly five of the six dice come up the same, the roll is called five-of-a-kind, and scores very well.
What is the probability of rolling five-of-a-kind on your first roll in Hex Yahtzee?
Explanation / Answer
(According to Chegg policy, only four subquestions will be answered. Please post the remaining in another question)
(a) If W = the set of all days of the week, and Y is the set of all words or names that end in
the letter y, how many elements are in the intersection of W and Y?
The intersection is the set of all days of the week whose names end in Y.
Since the names of all days of the week end in y, W Y = W.
(b) If B = the set of all birds currently swimming in the lake, and D = the set of all Ducks that are members of B, describe the set that is the complement of D in B.
Dc = Set of all birds that are currently swimming in the lake which are not ducks.
(c) If you draw 3 cards without looking at it from a standard 52-card deck designed for playing poker, what is the probability that all three cards will be Aces?
There are 4 aces out of 52 and so the probability of getting an ace on the first draw = 4/52
The probability of getting an ace on the second draw = 3/51
The probability of getting an ace on the second draw = 2/50
The probability of getting an ace on all three draws = 4/52 * 3/51 * 2/50
= 0.0002
(d) If you roll a standard six-sided die, what is the expectation of the number of dots on the top of the die?
The values for the die are 1,2,3,4,5,6.
Each value has probability 1/6
=> Expected value = 1/6 * (1 + 2 + 3 + 4 + 5 + 6)
= 21/6 = 3.5
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