Sharon has 24 colored paper clips in her desk drawer:12 are red, 8 are yellow, and 4 are blue. She also has 28 pushpins in her drawer: 11 are white, 14 are orange, and 3 are green.

1. If she picks one paper clip, what is the probability that it will be either blue or yellow.4/24*8/24=1/2
2. If she picks one paper clip and one push pin,what is the probability of picking a red paper clip and a push pin?12/24*11/28
3. If she picks two pushpins with replacement, what is the probability. of picking a green pushpin first and an oranges push pin second?

1. No, she picks only one clip

If we consider only the clips, there are 12 clips that are either blue or yellow, so the
prob(blue or yellow) = 12/24 = 1/2

I have ignored the pushpins, since I assume she is able to distinguish between paper clips and pushpins when randomly reaching in
I we allow that she may also choose a pushpin, then the above proability would be 12/52 =3/13

2. could be (red clip then push) or (push then red pin)
= (12/52)(28/51) + (28/52)(12/51)
= 2(28/221) = 56/221

3. prob( green, then orange pushpin) = (3/52)(14/52)
= 21/1352

The wording could be clearer.
e.g. in #2, your answer implies that you want a red clip and a red pushpin, and we would be able to distinguish between clips and pushpins in her desk
My answers reflect the second condition I stated in #1

To find the probability of picking a green pushpin first and an orange pushpin second, we should first calculate the probability of picking a green pushpin first and an orange pushpin second separately. Then, we multiply these probabilities together to find the overall probability.

1. Probability of picking a green pushpin first:
Given that there are 3 green pushpins out of a total of 28 pushpins, the probability of picking a green pushpin first is 3/28.

2. Probability of picking an orange pushpin second:
After picking the green pushpin (which we assumed was put back), there are still 28 pushpins in total, but now there are only 13 orange pushpins left. Therefore, the probability of picking an orange pushpin second is 13/28.

To find the overall probability, we multiply these probabilities together:
(3/28) * (13/28) = 39/784

So, the probability of picking a green pushpin first and an orange pushpin second, with replacement, is 39/784.