two six-sided dice are rolled; find prob. that they are both

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abarrien

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Two six-sided dice are rolled.

a) Find the probability that they are both 4's

My answer: 1/6*5/6+ 1/6*5/6 ?

b) Find the probability of rolling doubles

My answer: 1/6*1/6?

c) Find the probability of rolling a sum of at least 4, given that one of the dice was a two

My answer: 5/6*5/6?

d) If the sum was at least 9, find the probability that the sum was even

My answer: 4/6*4/6?
 
Re: two six-sided dice are rolled; find prob. that they are

abarrien said:
Two six-sided dice are rolled.

a) Find the probability that they are both 4's

My answer: 1/6*5/6+ 1/6*5/6 ? No: 1/36

b) Find the probability of rolling doubles

My answer: 1/6*1/6? No: 1/6

c) Find the probability of rolling a sum of at least 4, given that one of the dice was a two

My answer: 5/6*5/6? No, think again.

d) If the sum was at least 9, find the probability that the sum was even

My answer: 4/6*4/6? No, think again.
Click to expand...
 
Tossing two dice we get 36 ordered pairs:
(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)

Only the red ones fit are not in the ‘at least 4’ category.
Thus the answer is 33/36.
 
okay but since it says that one of them is a 2 , the answer is 9/36 right? and d is 4/36?
 
abarrien said:
okay but since it says that one of them is a 2 , the answer is 9/36 right? and d is 4/36?
Click to expand...
Yes that is correct!
 
marcmtlca said:
Are the dice fair?
Click to expand...
That is the usual assumption. And since that assumption seems to be leading to correct answers, it's probably safe to work under these conditions.

Eliz.
 
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