Probability, Selection, and Permutation Problems in Math Midterm Review
Prepare for your math midterm with these problems on probability, selection, and permutation. Solve questions involving selecting participants for a drug trial, finishing positions in a race, ordering pizza toppings, voter probabilities, and more.
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Math 21 Midterm Review Part 2: Chapters 5-7
13) In a drug trial there are 8 participants. In how many different ways can three of the participants be selected to receive a placebo? Selecting r out of n No repetition Does order of selection matter?
14) A sprint race has 12 runners in it. In how many different ways can the runners finish first, second, third, and fourth? Selecting r out of n No repetition Does order of selection matter?
15) A pizza restaurant has 5 different crusts available and 11 pizza toppings. Assuming that a customer cannot select the same topping more than once, in how many different ways can a customer order a 4-topping pizza?
16) The probability that a registered voter is female is 0.5. The probability that a registered voter is registered as an independent is 0.3. The probability that a registered voter is female and is registered as an independent is 0.2. a) Find the probability that a registered voter is female or independent.
16) The probability that a registered voter is female is 0.5. The probability that a registered voter is registered as an independent is 0.3. The probability that a registered voter is female and is registered as an independent is 0.2. b) If a randomly selected voter is a female, find the probability that she is registered as an independent.
17) Seven males and five females are to be interviewed for a job as a community college instructor. The top four candidates are sent forward to the president for a second interview. If all the candidates are equally qualified, find the probability that four females get a second interview.
18) A recent report stated that 84% of all elementary school teachers have a computer at home. If 12 elementary school teachers are selected at random, find the probability that 8 of them have a computer at home. n x Success p
19) Sixty percent of the students at a particular community college are female. If 13 students at that community college are selected at random, find the probability that between 5 and 10 students, inclusive, are female. n x Success p
20) Ten percent of the adults in a certain city hold a bachelors or higher degree. If 5 adults from this city are selected at random, find the probability that at least 3 do not have a bachelor s or higher degree. n x Success p
21) On a typical day at UC Santa Barbara there are 2.9 bike crashes per day. Find the probability that there will be 2 bike crashes on that campus today. t Mean x
22) On an average day there are 2 students absent from my math 21 class. Find the probability that 3 or more students are absent from my math 21 today. t Mean x
23) On average, the Fresno Grizzlies score 4.7 runs per game. Find the probability that the team scores exactly 11 runs in the next two games. t Mean x
24) The weights of salmon fillets at a fish market follow a normal distribution with a mean of 21 ounces and a standard deviation of 2.3 ounces. Find the probability that an individual salmon fillet will weigh more than 25 ounces. x
25) IQ scores are approximately normally distributed with a mean of 100 points, and a standard deviation of 15 points. Find the probability that a person has an IQ of 110 or lower. x
26) The heights of adult males are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. What height separates the shortest 15% of adult males from the rest? Tail %
28) Use a QQ Plot to determine whether the following data come from a population that is normally distributed. Times, in seconds, for greyhounds to run a 5/16-mile race. 31.26 31.35 31.91 32.06 32.37 32.52
