Roll two fair dice separately. Each dice has six faces. Let A be the event that either a three or four is rolled first, followed by an even number. Let B be the event that the sum of the two rolls is at most seven. Are A and B mutually exclusive events?Question 4Answera.Yesb.No
Question
Roll two fair dice separately. Each dice has six faces. Let A be the event that either a three or four is rolled first, followed by an even number. Let B be the event that the sum of the two rolls is at most seven. Are A and B mutually exclusive events?Question 4Answera.Yesb.No
Solution
To answer this question, we first need to understand what mutually exclusive events are. Mutually exclusive events are events that cannot occur at the same time. In other words, if one event occurs, the other cannot.
Event A: Either a three or four is rolled first, followed by an even number. This means the possible outcomes for event A are (3,2), (3,4), (3,6), (4,2), (4,4), (4,6).
Event B: The sum of the two rolls is at most seven. This means the possible outcomes for event B are (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (5,1), (5,2), (6,1).
If we look at the possible outcomes of both events, we can see that there are outcomes that can occur at the same time. For example, the outcome (3,2) can occur in both event A and event B.
Therefore, events A and B are not mutually exclusive. So, the answer is b. No.
Similar Questions
Roll two fair dice separately. Each dice has six faces. Let B be the event that the sum of the two rolls is at most seven. P(B) =
Two dice are rolled. Determine the probability of the following. (Enter your probabilities as fractions.)(a)rolling an even sum(b)rolling a sum greater than 7(c)rolling an even sum and a sum greater than 7(d)rolling an even sum or a sum greater than 7
Consider an experiment of rolling a fair four sided die twice where all the possible outcomes are equally likely. Define the eventsA = 1st roll results in a 1B = Sum of the two rolls is a 7C = 2nd roll results in a 2Which among the following statements are true?Events A and C are independent. Events A, B and C are mutually exclusive.Events A, B and C are exhaustive.P(A | (B ∪ C)) = 1/6
Three fair dice are thrown once. Given that no two dice show the same face.(a) What is the probability that the sum of faces is 7
QUESTION 8The numbers showing on the upper faces of two, fair, six-sided dice are observed when rolled. Consider events A and B defined as:A = the sum of the two values observed on the upper faces is at least 8 B = at least one dice has a 2 or less on the upper faceFind 1. P(B') (3 decimal places) 2. P(A or B) (3 decimal places)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.