Suppose that Eitan rolls a fair six-sided die and a fair four-sided die simultaneously. Let A be the event that the
sum of the dice is 8 and B be the event that Eitan rolls doubles. Using the sample space of possible outcomes
below, answer each of the following questions,
What is P(A), the probability that the sum of the dice is 8?
What is P(B), the probability that Eitan rolls doubles?
What is P(A and B), the probability that the sum of the dice is 8 and Eitan rolls doubles?
Are events A and B independent?
Choose 1 answer:
A Yes, events A and B are independent events.
No, events A and B are not independent events.

Given : Eitan rolls a fair six-sided die and a fair four-sided die simultaneously. A be the event that the sum of the dice is 8 and B be the event that Eitan rolls doubles

To find : probability of event A , event B , Event A or B , Event A & B

Solution:

Six Sides Dice has { 1 , 2 , 3 , 4 , 5 ,6 }

4 Sides Dice has = { 1 , 2 , 3 , 4 }

Total possible outcome = 6 * 4 = 24

n(S) = 24

A = Sum of Dice = 8

(4 , 4) , ( 5 , 3) , ( 6 , 2)

n(A) = 3

B = Double ( means same number on each Dice )

B = ( 1 , 1) , ( 2, 2) , ( 3 , 3) , ( 4, 4)

n(B) = 4

A U B = ( 1 , 1) , ( 2, 2) , ( 3 , 3) , ( 4, 4) ( 5 , 3) , ( 6 , 2)

n (A U B ) = { 6 }

A ∩ B = { 4 , 4}

n(A ∩ B) = 1

Probability of Event A = 3/24 = 1/8

probability of Event B = 4/24 = 1/6

Probability of Event A or B = 6/24 = 1/4

Probability of Event A and B = 1/24

Learn more:

You are given one 6 sided dice and an 8 sided dice. The 8 sided die

https://brainly.in/question/12351673

You roll a fair 666-sided die. What is ext{P(roll greater than 4})P(roll ...

https://brainly.in/question/16531574