SOLUTION: Hi there, please help with this: Consider rolling a fair 6-faced die twice. Let A be the event that the sum of the two rolls is at least 10, and B be the event that the first on

Algebra ->  Probability-and-statistics -> SOLUTION: Hi there, please help with this: Consider rolling a fair 6-faced die twice. Let A be the event that the sum of the two rolls is at least 10, and B be the event that the first on      Log On


   

Question 1052848: Hi there, please help with this:
Consider rolling a fair 6-faced die twice. Let A be the event that the sum of the two rolls is at least 10, and B be the event that the first one is a multiple of 3.
(a) What is the probability that the sum of the two rolls is at least 10 given that the first one is a multiple of 3?
(b) Are event A and event B independent? Explain.
Thank you so much!
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi  



(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)



(2,1) (2,2) (2,3) (2,4) (2,5) (2,6) 



(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) 



(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) 



(5,1) (5,2) (5,3) (5,4) (5,5) (5,6) 



(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)  Count them... 36 ways...3 qualify



(a) What is the probability that the sum of the two rolls is at least 10 given that the first one is a multiple of 3?  3/36 = 1/12

(b) Are event A and event B independent? Each roll of the Dice is Independent of the Other.

As to event A and event B being independent:

A the event that the sum of the two rolls is at least 10, 

and B the event that the first one is a multiple of 3. 

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Event A is dependent on the restraints of Event B