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Math 1121 Quiz 2 More Practice
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- A coin is to be tossed 1,000 times.
a) What is the probability that the 785th toss is heads?
b) What is the probability that the first and 20th tosses are both heads?
- Andrea did a survey in her statistics class and found that 18 students out of 30 use the library at least twice a week. (a) What is the probability that a student chosen at random from the class uses the library at least twice a week?
(b) What is the probability that a student chosen at random from the class uses the library less often than twice a week?
(c) If two students are chosen at random from the class what is the probability that both of them use the library at least twice a week?
(d) What is the probability that neither of them uses the library at least twice a week.
- You draw one card from a standard deck of 52 cards. 13 spades (2 through ace), 13 diamonds (2 through ace), 13 clubs (2 through ace), and 13 hearts (2 through ace).
(a) What is the probability that the card is the ace of spades?
(b) What is the probability that the card is a spade?
(c) What is the probability that the card is an ace or a spade?
- An urn contains 11 balls identical in every way except for color. There are 4 red balls, 5 green balls and 2 blue balls. (a) You draw two balls from the urn but replace the first before drawing the second. Find the probability that the first ball is red and the second ball is green.
(b) You draw two balls from the urn but do not replace the first ball before drawing the second. Find the probability that the first ball is red and the second ball is green.
(c) You draw two balls from the urn but do not replace the first ball before drawing the second. Find the probability of getting a red and a green ball in any order.
- (a) Seven equally qualified students apply for a scholarship, but only five scholarships, equal in value, can be given. How many ways can the five winners be selected?
(b) If the five scholarships are all different in value how many ways can the five winners be chosen?
- Student Life did a survey of students in which they asked if the person is a part-time student or a full-time student. They also asked if the person had voted in the most recent student election. The results follow:
If a student is selected at random from this group of 90 students, find the probability that: (a) The student voted in the most recent election.
(b) The student voted in the most recent election, given that the student is a part-time student.
(c) The student voted in the most recent election and the student is a part-time student.
- At Cape College the business students run an investment club. Each fall they create investment portfolios in multiples of $1,000 each. Records from the past several years show the following probabilities of profits (rounded to the nearest $50). In the table below, x = profit per $1,000 and P ( x ) is the probability of earning that profit.
(a) Find the expected value (mean) of the profit in a $1,000 portfolio.
(b) Find the standard deviation of the profit.
(c) What is the probability of a profit of $150 or more in a $1,000 portfolio?
- A fair coin is flipped three times. (a) Find the probability of getting exactly three heads.
(b) Find the probability of getting two or more heads.
(c) Find the probability of getting fewer than two heads.
(d) Find the probability of getting exactly two heads.
[5] (a) Number of winners = C (7,5) = 21 (b) Number of winners = P (7,5) = 2,
Reference: [4.83] [6] (a) P (student voted) = 0. (b) P (student voted, given part-time student) = 0. (c) P (part-time student and student voted) = 0. . Reference: [5.33] [7] (a) Expected profit = $82. (b) Standard deviation = $55. (c) P (profit ≥ $150) = 0.
Reference: [5.64] [8] n = 3, p = 0. (a) P (exactly three heads) = 0. (b) P (two or more heads) = 0. (c) P (fewer than two heads) = 0. (d) P (exactly two heads) = 0.
Reference: [5.81]
[10] (a)
(b) Expected number to request main-floor seating = 2. (c) Standard deviation = 1.
Reference: [5.86] [10] a) 1/40 =. b) 1/38 =. c) lose 1st, lose 2nd, win 3rd d) 1/40 =.
