Independent and Mutually Exclusive Events: example 3.13
Toss one fair coin (the coin has two sides, H and T). The outcomes are ________. Count the outcomes. There are ________ outcomes.
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.
Multiply the two numbers of outcomes. The answer is ________.
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.
Event A = heads (H) on the coin followed by an even number (2, 4, 6) on the die.
A = {________}. Find P(A).
Event B = heads on the coin followed by a three on the die. B = {________}. Find P(B).
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.
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.
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
1
Solution
H and T; 2
1, 2, 3, 4, 5, 6; 6
2(6) = 12
Make a systematic list of possible outcomes. Start by listing all possible outcomes when the coin shows tails (T). Then list the outcomes that are possible when the coin shows heads (H): T1, T2, T3, T4, T5, T6, H1, H2, H3, H4, H5, H6
A = {H2, H4, H6}; P(A) =
=
B = {H3}; P(B) =
Yes, because P(A AND B) = 0
P(A AND B) = 0. P(A)P(B) = . P(A AND B) does not equal P(A)P(B), so A and B are dependent.