Probability & Statistics Exam Questions with Verified Solutions Rated 100%

Probability & Statistics Exam Questions with Verified Solutions Rated 100% A carpet store allows customers to choose carpet based on color, thread type, and thickness. If a customer can choose among 5 colors, 3 thread types, and 3 thicknesses, how many different types of carpet could the customer choose? - Answers 45 Horace owns 9 science books, 12 poetry books, and 6 novels. How many total books does he own? - Answers 27 Evaluate the following expression. 7!4!3! - Answers 35 There are 12 candidates running for any of 6 distinct positions in a school's student council. In how many different ways could the 6 positions be filled? - Answers 12!/6! = 665280 How many distinct rearrangements of the letters in "tweedledee" are there? Give your answer as an integer. - Answers 15120 A track race has 6 participants. In how many orders could the runners possibly finish? - Answers 720 Victor will choose 6 colors to use for an art project. If there are 12 colors to choose from, how many different color combinations are possible? - Answers 924 A car dealership offers 10 different upgrades with each of the vehicles it sells. If a customer can choose any number of upgrades offered, how many upgrade combinations are possible? - Answers 1024 A particular 3rd grade class has 20 students. When the teacher checks attendance for the day, 3 are sick and 1 spends the day in the principal's office. Assuming this is the normal occurrence for each day, what is the empirical probability that a student is not in class? Write your answer as an exact fraction which is reduced as much as possible. - Answers 0.2 A bag of marbles contains 6 green marbles, 10 purple marbles, and 8 yellow marbles. What is the probability that a marble picked at random is green? Give your answer as a simplified fraction. - Answers 1/4 A pet store has the top 8 ranked dog toys. What are the chances that your dog chooses the top-ranked dog toy first and the second top-ranked dog toy second? Write your answer as an exact fraction which is reduced as much as possible. - Answers 1/56 An elementary school art class teacher plans to display artwork next to the door of each of the classrooms in the school. Each classroom door will only have one piece of artwork displayed, and the school has 37 such doors. If the teacher has 22 sculptures and 22 oil paintings, what is the probability that 20 sculptures and 17 oil paintings are chosen to be displayed? - Answers (22/20)(22/17)/(44/37) A spinner contains the numbers 1 through 50. What is the probability that the spinner will land on a number that is not a multiple of 6? Give your answer as a simplified fraction. - Answers 21/25 A coin is tossed 6 times. Find the probability that a heads is flipped at least once. Round your answer to two decimal places. - Answers 0.98 A person chooses a single state from all 50 states in the United States. Find the set representing the event E that state starts with an H. - Answers Hawaii A person chooses 1 odd number between 3 to 9 inclusive. What is the sample space in this experiment? - Answers S= { 3, 4, 5, 6, 7, 8, 9} If a card is picked at random from a standard 52-card deck, what is the probability of getting a black card or a Queen? - Answers 7/13 Suppose you took a poll of kids that like cookies. Out of 10 kids, 7 like cookies. You put each of their names in a bag and randomly draw a name, then replace the name and draw again. If you pull 3 names from the bag and replace them after each draw, what is the probability each name drawn likes cookies? Round to the nearest thousandths. - Answers 0.343 C and D are two events with P(C)=0.4,P(D)=0.5, and P(C|D)=0.4. Calculate P(D|C). Give your answer as a decimal to the tenths place. - Answers 0.5 A survey of households owned by couples was done. It found the number of children couples had in each household. The following probability distribution of the random variable X was created from that survey. What is the probability of more than two children in a household? X-valueP(X)-00.1310.420.3130.1140.05 Write your answer as a decimal. - Answers 0.16 Let N be a random variable defined as the number of days of paid vacation for people in the U.S. Let's suppose A statistician comes up with the following probability function for N: fN(n)={0.15 for n=0,0.15 for n=5,0.35 for n=8,0.1 for n=10, and 0.25 for n=12}. What is the expected value of N? Give your answer as a decimal. - Answers 7.55 True or False? In reference to different sampling methods, systematic sampling includes the steps: divide the population into groups; use simple random sampling to identify a proportionate number of individuals from each group. - Answers False