Help me with these logic problems!?

Question

HW 1: Suppose we have two regular tetrahedrons, one blue and one red, and the vertices of each are numbered 1 through 4, so that when we roll each tetrahedron, each of the four numbers is equally likely to appear as the top vertex. Such tetrahedrons are essentially four-sided dice. How many possible outcomes are there when we roll these two dice?


HW 2: What is the probability that both die will show the same number?


HW 3: What is the probability that the sum of the numbers on the dice will be 3?


HW 4: What is the probability that at least one of the dice will show a 1?


HW 5: A school has a fund-raising raffle. 500 tickets are sold for $10 each. One grand prize of $1000 is awarded to the w inning ticket. What is your probability of winning the grand prize if you buy 10 tickets?

HW 6: If, in problem 5 there are two grand prizes, what are your chances of winning at least one of the two prizes if you buy 10 tickets? (Hint: think about this carefully. It may help to think about how you would calculate your chances of not winning either prize first.)

HW 7: Suppose a dart board is divided into three pie-shaped sections emanating from the center. The central angle of section A is 45 degrees, of Section B is 135 degrees, and Section C is 180 degrees. Given that a dart lands somewhere on the board, we assume that it is equally likely to land in at any given point on the board. What is the probability that it will land in each of the three sections?

HW 8: What is the probability that, if we throw three darts, they will all land in Section A?

HW 9: What is the probability that if we throw two darts, one will land in each of sections A and C?

HW 10: If you draw two cards from a full deck of 52 standard playing cards, what is the probability that they will be a pair?


HW 11: If you draw two cards from a full deck of 52 standard playing cards, what is the probability that they will be a pair of Jacks?

Answer 1

1. 4 x 4 = 16
2. 1 chance in 4 or 25%
3. Only a combination of 1 & 2 will work.
That's 2 out of 16 or 12.5%
4. 1 chance in 16 or 6.25%
5. 10 out of 500 or 2.0%
6. I'm tired

Answer 2

HW 1: Suppose we have two regular tetrahedrons, one blue and one red, and the vertices of each are numbered 1 through 4, so that when we roll each tetrahedron, each of the four numbers is equally likely to appear as the top vertex. Such tetrahedrons are essentially four-sided dice. How many possible outcomes are there when we roll these two dice?

you can get: (11, by this arrangement I mean getting 1 on the first tetrahedron and also getting 1 on the second tetrahedron, 12 means getting 1 on first tetrahedron and 2 on the second tetrahedron)

11; 12;13;14;21;22;23;24;31;32;33;34;41;42;43;44
so there are 4*4 = 16 possibilties

HW 2: What is the probability that both die will show the same number?
=4/16 = 1/4

HW 3: What is the probability that the sum of the numbers on the dice will be 3?
=2/16 = 1/8

HW 4: What is the probability that at least one of the dice will show a 1?
=7/16

HW 5: A school has a fund-raising raffle. 500 tickets are sold for $10 each. One grand prize of $1000 is awarded to the w inning ticket. What is your probability of winning the grand prize if you buy 10 tickets?
=10/500 = 1/50

HW 6: If, in problem 5 there are two grand prizes, what are your chances of winning at least one of the two prizes if you buy 10 tickets? (Hint: think about this carefully. It may help to think about how you would calculate your chances of not winning either prize first.)
=10/500 + 10/499 = .04 or 4%

HW 7: Suppose a dart board is divided into three pie-shaped sections emanating from the center. The central angle of section A is 45 degrees, of Section B is 135 degrees, and Section C is 180 degrees. Given that a dart lands somewhere on the board, we assume that it is equally likely to land in at any given point on the board. What is the probability that it will land in each of the three sections?
P(A) = 45/360 = .125
P(B) = 135/360 = .375
P(C) = 180/360 = 1/2 = .5

HW 8: What is the probability that, if we throw three darts, they will all land in Section A?
=(.125)^3 = .0019

HW 9: What is the probability that if we throw two darts, one will land in each of sections A and C?
P(A & C) =.125*.5 = .0625

HW 10: If you draw two cards from a full deck of 52 standard playing cards, what is the probability that they will be a pair?
=(4/52)*(3/51) = .0045

HW 11: If you draw two cards from a full deck of 52 standard playing cards, what is the probability that they will be a pair of Jacks?
=(4/52)*(3/51) = .0045 (same as before, because it does not matter if it is a jack or queen or ace, probability of getting a pair is .0045)