Independent and Mutually Exclusive Events · Example 7
(a) Toss one fair coin (the coin has two sides, H and T). The outcomes are ________. Count the outcomes. There are ________ outcomes.
(b) 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.
(c) Multiply the two numbers of outcomes. The answer is ________.
(d) 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). List the outcomes. Hint—Two of the outcomes are H1 and T6.
(e) Event A = heads (H) on the coin followed by an even number (2, 4, 6) on the die.
A = {________}. Find P(A).
(f) Event B = heads on the coin followed by a three on the die. B = {________}. Find P(B).
(g) 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.
(h) 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, Statistics · §3.2 Independent and Mutually Exclusive Events · Example 7
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