Question

Please help me with these questions and please show the work or something... and yep, 30 points so you better answer with an explanation:
-Picking a red checker from a bag of 9 black checkers and 6 red checkers, replacing it, and picking another red checker. I said 4/25.

-Picking a black checker from a bag of 9 black checkers and 6 red checkers, replacing it, and picking another red checker. I said 6/25.

-Picking a black checker from a bag of 9 black checkers and 6 red checkers, replacing it, and picking another black checker.

-Rolling a 6 on the first roll of a 1-6 number cube and rolling a 3 on the second roll of the same cube.

-Rolling a 6 on the first roll of 1-6 number cube and rolling a 7 on the second roll of the same cube.

-Rolling a 1, 2, or 3 on the first roll of a 1-6 number cube and rolling a 4, 5, or 6 on the second roll of the same cube.

Answer 1

Part 1:

You have the correct answer. You multiply the probability of getting red (6/15) by the probailitiy of getting red (6/15) to get 36/225 which reduces to 4/25

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Part 2: 

This is also correct. Nice work. You multiply the probability of getting black (9/15) with the probability of getting red (6/15) to get 54/225 = 6/25

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Part 3:

The probability of picking a black checker is 9/15. If a replacement is made, then the probability of picking another black checker is also 9/15. So, 

(9/15)*(9/15) = 81/225 = 9/25

Answer: 9/25

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Part 4:

The probability of rolling a 6 is 1/6. The probability of rolling a 3 is 1/6 as well. This is because there is only one side with this label out of 6 total. Multiply the probabilities

(1/6)*(1/6) = 1/36

Answer: 1/36

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Part 5:

It is impossible to roll a 7 on the six sided cube because the highest number is 6. Therefore the overall probability is 0

Answer: 0

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Part 6:

There are 3 outcomes we want (rolling a 1,2, or 3) out of 6 total. So the probability of rolling a 1,2 or 3 is 3/6 = 1/2. Similarly, the probability of rolling a 4, 5 or 6 is 3/6 = 1/2 as well.

Multiplying the probabilities gives

(1/2)*(1/2) = 1/4

Answer: 1/4