You roll two fair dice, one green and one red.(a) Are the outcomes on the dice independent?(b) Find P(4 on green die and 6 on red die).(c) Find P(6 on green die and 4 on red die).(d) Find P((4 on green die and 6 on red die) or (6 on green die and 4 on red die)). Step 4First find P(4 on green die).There are six faces on a die, and on a fair die each face is equally likely to come up when we roll the die.Recall the formula for the probability of an event with equally likely outcomes.number of outcomes favorable to eventprobability of eventtotal number of outcomesWhen we roll the green die there aretotal possible outcomes. Of those total possibleoutcomes, only the one outcome where we roll a 4 is favorable to the event "4 on green die". Therefore, wehave the following result.number of outcomes where a 4 is showing on green dieP(4 on green die)total number of possible outcomes when green die is rolled1Using the same method, find the probability of the other event.number of outcomes where a 6 is showing on red dieP(6 on red die)%3Dtotal number of possible outcomes when red die is rolled16.SubmitSkip (you cannot come back).

(a) Thus, the event of getting any number in green die is independent of getting any number from 1 to 6 in red die and vice versa. However, all the numbers of both green and red dice are mutually exclusive for their own case, i.e. if we get "2" in die green all the rest numbers of 1,3,4,5,6 are excluded from appearing in the green die. Same is the case with the red die. (b) P(4 on the green die and 6 on the red die) P(4 on the green die)= 16 P(6 on the red die) = 16 Since bot the events are independent. We have, P(4 on green die and 6 on red die) = P(4 on green die) . P(6 on red die) =16 x16=136 (c) P(6 on the green die and 4 on the red die) P(6 on the green die)= 16 P(4 on the red die) = 16 Since bot the events are independent. We have, P(6 on green die and 4 on red die) = P(6 on green die) . P(4 on red die) =16 x16=136 Since you have posted a question with multiple subparts, we will solve the first 3 subparts for you. To get the remaining subpart done please repost the -–- question and mention the subparts to be solved.

Answered: u roll two fair dice, one green and one…

Math

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u roll two fair dice, one green and one red. (a) Are the outcomes on the dice independent? (b) Find P(4 on green die and 6 on red die). (c) Find P(6 on green die and 4 on red die).

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

100%

You roll two fair dice, one green and one red.
(a) Are the outcomes on the dice independent?
(b) Find P(4 on green die and 6 on red die).
(c) Find P(6 on green die and 4 on red die).
(d) Find P((4 on green die and 6 on red die) or (6 on green die and 4 on red die)).

Step 4
First find P(4 on green die).
There are six faces on a die, and on a fair die each face is equally likely to come up when we roll the die.
Recall the formula for the probability of an event with equally likely outcomes.
number of outcomes favorable to event
probability of event
total number of outcomes
When we roll the green die there are
total possible outcomes. Of those total possible
outcomes, only the one outcome where we roll a 4 is favorable to the event "4 on green die". Therefore, we
have the following result.
number of outcomes where a 4 is showing on green die
P(4 on green die)
total number of possible outcomes when green die is rolled
1
Using the same method, find the probability of the other event.
number of outcomes where a 6 is showing on red die
P(6 on red die)
%3D
total number of possible outcomes when red die is rolled
1
6.
Submit
Skip (you cannot come back).

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