8-8: Mixed Practice

A simulator randomly selects a letter from the word CHIMPANZEE. Fred ran the simulator 1,000 times

And got a vowel 600 times.

• The simulator selected a vowel 400 fewer times than the Theoretical Probability.

• The simulator selected a vowel 200 fewer times than the Theoretical Probability.

• The simulator selected a vowel 200 more times than the Theoretical Probability.

• The simulator selected a vowel 400 more times than the Theoretical Probability.

Use the numbers 1 through 20 as a sample space for the sets of numbers described below.

X = {multiples of 2}

Y = {multiples of 3}

Z = {factors of 6}

Which statement is true?

• The union of Y and Z is no solution

• The intersection of Y and Z is {3,6}

• The union of X and Y is {6, 12,18}

• The intersection of X, Y, and Z is {2,3,4,6,8,9,10}

A book club has 400 members. Each member was asked whether he or she prefers fiction or non-fiction books. The results are shown in the relative frequency table below. Which statement is true?

• 20 more 31-40 year olds than 21-30 year olds prefer fiction

• 150 members are 31-40 and prefer fiction

• 172 members are 21-30 years old.

• 260 members prefer fiction.

Which event could BEST be represented with a conditional probability statement?

• The probability that a coin toss is heads given that the first toss was tails

• The probability that the number on a fair number cube is odd given that a fair spinner is spun

• The probability that a card drawn from a regular deck of 52 cards is a diamond given that the card is a red card.

• The probability that a random number generator shows an odd number given that the first number generated was odd.

Kim tosses a coin multiple times and records the outcomes. Which statement is always true?

• For the first 10 tosses, the experimental probability of the coin landing heads up will be less than the theoretical probability.

• For the first two tosses, the experimental probability of the coin landing heads up will be different from the theoretical probability.

• As the number of tosses increases, the difference between the experimental and theoretical probabilities decreases.

• As the number of tosses increases, the difference between the experimental and theoretical probabilities increases.

A survey was conducted to find out what percentage of students like Pizza or Tacos or Both. Students had to select one of those three options. Let A represent the students who like Pizza and B represent the set of students who like Tacos. Which statement correctly describes the complement of set B?

• The students who prefer pizza or tacos or both.

• The students who prefer only pizza or only tacos.

• The students who prefer tacos but but pizza.

• The students who prefer only pizza.

Suppose 60% of all households in a community have a dog. Of all households, 32% have a dog and a cat. What is the approximate probability that a household in the community has a cat, given that it has a dog?

• 53%

• 47%

• 28%

• 19%

Three sets are defined as follows.

W: {even integers}

X: {multiples of 3}

Z: {W ∩ X}

Which choice is an element of Z?

• -9

• -8

• -7

• -6

A short quiz consists of five multiple-choice questions, each with four possible answer choices. Only one answer choice is correct. If a student takes the quiz and randomly guesses on the first four questions, what is the probability that the answer choices for all four questions are incorrect?

• 32%

• 0.3%

• 3%

• 17%

A game comes with a deck of cards with each card showing one of the numbers 2, 3, 4, 5, 6, or 8. Each card occurs one time in orange, one time in purple, and one time in green. Given that an orange card is drawn, what is the probability that the card is a 3?

• 14%

• 17%

• 13%

• 38%