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 to c is the number of outcomes (size of the sample space). What are 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 $P\left(A\cap B\right)$? If $P\left(A\cap B\right)=0$, then A and B are mutually exclusive.)
(h) Are A and B independent? (Hint: Is $P\left(A\cap B\right)=P\left(A\right)P\left(B\right)$? If $P\left(A\cap B\right)=P\left(A\right)P\left(B\right)$, then A and B are independent. If not, then they are dependent).

OpenStax, Introductory Business Statistics 2e · §3.2 Independent and Mutually Exclusive Events · Example 7