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Introduction to Probability · Ages 15–16

Addition Rule and Disjoint Events Practice

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Determine whether each pair of events is disjoint, then calculate the probability of their union. Express all final answers as simplified fractions.

  1. A standard six-sided die is rolled. Event A is rolling a 2. Event B is rolling a 5. Are the events disjoint? Find P(A or B).

  2. A standard six-sided die is rolled. Event A is rolling an even number. Event B is rolling a number greater than 4. Are the events disjoint? Find P(A or B).

  3. A card is drawn from a standard deck of 52 cards. Event A is drawing a King. Event B is drawing a Queen. Are the events disjoint? Find P(A or B).

  4. A card is drawn from a standard deck of 52 cards. Event A is drawing a Heart. Event B is drawing an Ace. Are the events disjoint? Find P(A or B).

  5. A ticket is selected at random from tickets numbered 1 to 20. Event A is drawing a multiple of 4. Event B is drawing an odd number. Are the events disjoint? Find P(A or B).

  6. In a group of 30 students, 18 take Spanish, 12 take Art, and 6 take both. Find the probability that a randomly chosen student takes Spanish or Art.

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Addition Rule and Disjoint Events Practice

Answer key

  1. A standard six-sided die is rolled. Event A is rolling a 2. Event B is rolling a 5. Are the events disjoint? Find P(A or B).

    Yes, disjoint. P(A or B) = 1/6 + 1/6 = 2/6 = 1/3.

  2. A standard six-sided die is rolled. Event A is rolling an even number. Event B is rolling a number greater than 4. Are the events disjoint? Find P(A or B).

    No, not disjoint (6 is in both). P(A or B) = 3/6 + 2/6 - 1/6 = 4/6 = 2/3.

  3. A card is drawn from a standard deck of 52 cards. Event A is drawing a King. Event B is drawing a Queen. Are the events disjoint? Find P(A or B).

    Yes, disjoint. P(A or B) = 4/52 + 4/52 = 8/52 = 2/13.

  4. A card is drawn from a standard deck of 52 cards. Event A is drawing a Heart. Event B is drawing an Ace. Are the events disjoint? Find P(A or B).

    No, not disjoint (the Ace of Hearts is in both). P(A or B) = 13/52 + 4/52 - 1/52 = 16/52 = 4/13.

  5. A ticket is selected at random from tickets numbered 1 to 20. Event A is drawing a multiple of 4. Event B is drawing an odd number. Are the events disjoint? Find P(A or B).

    Yes, disjoint (multiples of 4 are all even). P(A or B) = 5/20 + 10/20 = 15/20 = 3/4.

  6. In a group of 30 students, 18 take Spanish, 12 take Art, and 6 take both. Find the probability that a randomly chosen student takes Spanish or Art.

    No, not disjoint. P(Spanish or Art) = 18/30 + 12/30 - 6/30 = 24/30 = 4/5.