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Back to 3.2 Independent and Mutually Exclusive Events

3.2 Exercise 17

Avg difficulty 2.5
  1. Toss one fair coin (the coin has two sides, H and T). The outcomes are ________. Count the outcomes. There are ____ outcomes.
  2. Toss one fair, six-sided die (the die has 1, 2, 3, 4, 5 or 6 dots on a side). The outcomes are ________________. Count the outcomes. There are ___ outcomes.
  3. Multiply the two numbers of outcomes. The answer is _______.
  4. If you flip one fair coin and follow it with the toss of one fair, six-sided die, the answer in part c. is the number of outcomes (size of the sample space). What are the outcomes? (Hint: Two of the outcomes are H1 and T6.)
  5. Event A = heads (H) on the coin followed by an even number (2, 4, 6) on the die.
    A = {_________________}. Find P(A).
  6. Event B = heads on the coin followed by a three on the die. B = {________}. Find P(B).
  7. Are A and B mutually exclusive? (Hint: What is P(A AND B)? If P(A AND B) = 0, then A and B are mutually exclusive.)
  8. Are A and B independent? (Hint: Is P(A AND B) = P(A)P(B)? If P(A AND B) = P(A)P(B), then A and B are independent. If not, then they are dependent).

OpenStax Introductory Statistics 2e, 3.2 Independent and Mutually Exclusive Events, exercise 17

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Adapted from Introductory Statistics 2e © 2023 Rice University. Licensed under CC BY 4.0. Source: Introductory Statistics 2e. Imported at revision 50ec917.