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.
Answers
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
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