A vase has 3 blue marbles, 4 red marbles, 2 yellow marbles, and 1 purple marble.

ID: 3225365 • Letter: A

Question

A vase has 3 blue marbles, 4 red marbles, 2 yellow marbles, and 1 purple marble. Assume sampling without replacement, unless otherwise noted.

show step by steps and write clear please.

a. If you draw two marbles at random, what is the probability that they are the same color?

b. If you draw two marbles at random, what is the probability that they are different colors?

c. If you draw four marbles at random, with replacement, what is the probability that none are red?

d. If you were to take all of the marbles out of the vase and string them together, how many different patterns could you create?

Answer in detail with exaplanation below:

1. You pick 2 color , same color marbles ?

= 3C2+ 4C2 + 2C2 / 10*9

= 3+6+1 / 90

= 1/9

2. The answer is P( different color) = 1- P(same color) = 1- 1/9 = 8/9

3, P( none is red) = 6C4 / 10C4 = .071429

4. If you string them together the no. of patterns = 10! / 4!2!3!1!) = 288

I have divided by 4!,3!,2! becuase they are same colored marbles, which won't contribute to "different patterns" of marble string.

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