1) A bagel shop offers 14 varieties of bagels, 11 flavors of cream cheese, and 15 flavors of coffee. How many different orders for a bagel, cream cheese, and a coffee can a customer place?
2) 2800 people were surveyed about their recent purchases. 715 of those people surveyed bought a television within the last year, 461 bought a video game system within the last year, and 292 bought both.
a) How many people didn't buy either one?
b) How many people bought at least one of the two?
3) A 7-character password consists of three letters (from A to Z) followed by four numbers (from 1 to 9).
a) How many different passwords can be formed?
b) How many different passwords have no repeated number or letters?
4) Twelve cards are marked with the numbers 1 - 12, shuffled, and 4 cards are then drawn.
a) How many different 4-card hands are possible?
b) How many different 4-card hands contain a number less than 7?
5) Raskin-Bobbins, a knock-off ice cream store, advertises that it has 37 flavors of ice cream.
a) How many different triple-scoop cones can be made if the flavors can be duplicated?
b) How many different triple-scoop cones can be made if none of the flavors can be duplicated and the order of the flavors doesn't matter?
6) A legislative committee consists of 8 Democrats, 6 Republicans, and 1 Independent. A delegation of 3 is selected to visit a small Pacific island republic:
a) How many different delegations are possible?
b) How many different delegations consist of at least 1 Republican?
7) Suppose an exam has 28 questions on it and students need to answer 18 of the questions. How many ways can this be done if the first 5 and the last 4 questions must be answered and question #19 must not be answered because of a typo?
8) Suppose that a pair of 20-sided dice are rolled (the sides are numbered 1-20).
a) What is the probability that the sum of the dice is 13?
b) What is the probability that the sum of the dice is at least 36?
c) What is the probability that the sum is divisible by 10?
9) A box contains 4 green, 10 red, 6 yellow, and 5 blue marbles. Four marbles are drawn from the box without replacement.
a) What is the probability that you get one marble of each color??
b) What is the probability that none of the marbles is red?
c) What is the probability that all four marbles are the same color
10) A bicycle plant runs two assembly lines, A and B. 96.3% of line A's products pass instruction, while only 92.1% of line B's products pass inspection, and 70% of the factory's bikes come off assembly line A.
a) What is the probability that a randomly selected bike passed inspection?
b) What is the probability that a randomly selected bike that did not pass inspection came from assembly line B?
11) Two students, Jen and John, are registered for the same class and attend independently to each other, Jen 82.5% of the time and John 95% of the time. What is the probability that on any given day
a) Both will be in class?
b) At least one of them will not be in class?
12) In a study to determine frequency and dependency of color-blindness relative to females and males, people were chosen at random and the following results were recorded: Female Male
Color-Blind 7 44
Not Color-Blind 619 583
In this solution twelve examples are worked out. The problems are relating to permutations and combinations, computation of probability, addition theorem, conditional probability, theorem on total probability, Bayes theorem and chi square test for independence
Three questions on probability
1) Researchers at a pharmaceutical company have found that the effective time duration of a safe dosage of a pain relief drug is normally distributed with mean 2 hours and standard deviation 0.3 hour. For a patient selected at random:
a) What is the probability that the drug will be effective for 2 hours or less?
b) 1 hour or less?
c) 3 hours or more?
2) Life span for red foxes follow an approximately normal distribution with mean 7 years and standard deviation 3.5 years.
a) Find the probability that a red fox chosen at random will live at least 10 years.
b) Find the probability that a random sample of 4 red foxes will have a sample mean life span of over 10 years.
3) Margot has found that the mean time to run a job at the college copy center is 12.6 minutes with standard deviation 10 minutes. She selects a random sample of 64 jobs.
a) What is the probability that the sample mean copying time is between 14 and 15 minutes?
b) What is the probability that the sample mean copying time for this sample is between 10 and 12 minutes?