Sample Space Question (Algebra 2) [Probability]

[cammy_]

Hey everyone, I needed help solving this problem for an assignment, I literally have no clue how to solve it. It's worth 10 points so it would mean a lot if someone could help me do it.

 

[Harry_the_cat]

Can you find P(A), P(B), P(C) and P(D)?

 

[cammy_]

Can you find P(A), P(B), P(C) and P(D)?

a= (1,1) (1,3) (2,1) (2,3) (3,1) (3,3) (4,1) (4,3)
b= (1,1) (1,2) (1,3) (1,4) (3,1) (3,2) (3,3) (3,4)
c= (1,2) (1,3) (2,2) (2,3) (3,2) (3,3) (4,2) (4,3)
d= (1,1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (2,4)

Yes, I can

 

[Dr.Peterson]

You haven't actually calculated the probabilities yet, but those are the events being asked about (except that C is slightly wrong, and D looks like you misread the description).

Once you fix those, you can find the probabilities; but it may be more useful to just use those as background, and repeat the process with the events asked for. Can you list the outcomes that constitute the requested intersection, union, and complement?

That is, what are the sets [MATH]A\cap B[/MATH], [MATH]B\cup C[/MATH], and [MATH]D'[/MATH]?

 

[Steven G]

a= (1,1) (1,3) (2,1) (2,3) (3,1) (3,3) (4,1) (4,3)
b= (1,1) (1,2) (1,3) (1,4) (3,1) (3,2) (3,3) (3,4)
c= (1,2) (1,3) (2,2) (2,3) (3,2) (3,3) (4,2) (4,3)
d= (1,1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (2,4)

Yes, I can

a) the sum of the two dice must be ODD. (1,1)-sum is 2, (1,3)-sum is 4, (3,1)-sum is 4, (3,3)-sum is 6
b) correct
c) 2 IS prime, so include (1,1). (1,3)-sum is 4 and 4 is not prime. (1,4)-sum is 5 and 5 is prime. Include (2,1), (4,1). Don't include (2,2), (3,3), (4,2)
d)(1,1) (1,2) (1,3) (1,4)--sorry but the 1st die is always 1 and 1 is NOT greater than or equal to 2. Include (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3) and (4,4) as 3 and 4 (the values for the 1st die) are all greater than 2