Theoretical/Empirical Probabilities

A fair coin is flipped 500 times, with 275 heads and 225 tails. What is the theoretical probability the next coin flip is heads?

• 𝑃(𝐻𝑒𝑎𝑑𝑠) = 0.45

• 𝑃(𝐻𝑒𝑎𝑑𝑠) = 0.5

• 𝑃(𝐻𝑒𝑎𝑑𝑠) = 0.55

• 𝑃(𝐻𝑒𝑎𝑑𝑠) = 0.6

Tags

HSS.MD.A.3

A die is rolled 200 times, with the following probability distribution. Which of the following expressions is true for the theoretical probability of the next die roll? Select all that apply.

• 𝑃(1) = 𝑃(6)

• 𝑃(2) > 𝑃(5)

• 𝑃(3) < 𝑃(4)

• 𝑃(2) = 𝑃(5)

Tags

HSS.MD.A.3

Which of the following is true for theoretical probabilities? Select all that apply.

• They are calculated by dividing the number of experiments by the number of outcomes.

• They are calculated by dividing the number of trials by the number of outcomes.

• They are influenced by experimental data and/or past outcomes.

• Every outcome has a defined or inherently equal probability of occurring.

Tags

HSS.MD.A.3

Four cards are drawn (with replacement) from a standard deck of cards. If a card is a spade, you gain 10 dollars. If it is not, you lose 4 dollars. What is the probability distribution for this game? (Values rounded to the nearest thousandth.)

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Tags

HSS.MD.A.3

A random number generator chooses integers between 0 and 9 with equal probabilities. If X is a discrete random variable representing the integer chosen, what is E(X)?

• E(X) = 4

• E(X) = 4.5

• E(X) = 5

• E(X) = 5.5

Tags

HSS.MD.A.3

A fair coin is flipped 50 times, with 28 heads and 22 tails. What is the empirical probability the next coin flip is tails?

• 𝑃(𝑇𝑎𝑖𝑙𝑠) = 0.22

• 𝑃(𝑇𝑎𝑖𝑙𝑠) = 0.44

• 𝑃(𝑇𝑎𝑖𝑙𝑠) = 0.50

• 𝑃(𝑇𝑎𝑖𝑙𝑠) = 0.56

Tags

HSS.MD.A.4

A fair die is rolled 100 times, with the following probability distribution. Which of the following statements about expected values is true?

• The theoretical expected value is larger than the empirical expected value.

• The empirical expected value is larger than the theoretical expected value.

• The theoretical and empirical expected values are equal.

• It is impossible to calculate the theoretical expected value.

Tags

HSS.MD.A.4

Which of the following is true for empirical probabilities? Select all that apply.

• They are based on inherent assumptions about the scenario.

• They are based on previously collected data.

• They are calculated by dividing past successes by past outcomes.

• They are calculated by dividing past outcomes by past successes.

Tags

HSS.MD.A.4

Four cards are drawn (with replacement) from a standard deck of cards, with the results being: 5 of Spades, K of Diamonds , 7 of Hearts , K of Spades . Which of the following probabilities is empirical? Select all that apply.

• P(Spades) = 1/4

• P(Diamonds) = 1/4

• P(K) = 1/2

• P(7) = 1/13

Tags

HSS.MD.A.4

For which of the following scenarios would empirical probabilities likely be most helpful? Select all that apply.

• Probability of getting tails on a weighted, unfair coin.

• Probability of spinning green on a spinner with four equal-sized colors.

• Probability of picking a blue marble out of a bag with a known amount of several marbles.

• Probability of facing heavy traffic on your way home from school.

Tags

HSS.MD.A.4