Question

Suppose that marvin rolls a pair of fair six-sided dice. Let \[a\] be the event that the first die lands on \[4\] and \[b\] be the event that marvin rolls doubles. using the sample space of possible outcomes below, answer each of the following questions.

Answer 1

a. The sample space for rolling a die and tossing a coin consists of all possible outcomes of these two events. b. Event A is the event that either a three or a four is rolled first, followed by a head on the coin toss. The probability of event A is 1/6. c. Event B is the event that both tosses land on heads. Events A and B are not mutually exclusive.

Step-by-step explanation:

a. The sample space for rolling a die and tossing a coin consists of all possible outcomes of these two events. The sample space can be listed as:

{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)}

b. Event A is the event that either a three or a four is rolled first, followed by a head on the coin toss. The outcomes that satisfy event A are {(3, H), (4, H)}. Therefore, the probability of event A is P(A) = 2/12 = 1/6.

c. Event B is the event that both tosses land on heads. The outcome that satisfies event B is {(H, H)}. Since event A and event B do not have any common outcomes, they are mutually exclusive. Therefore, the events A and B are not mutually exclusive.