MAT 142: An urn contains 33 balls. Twelve are black, 11 are

Due to an injury, I wasnt able to make it to class the past week. Long story short, my teacher isn't responding to my requests for help, and I'm having trouble trying to learn from the book. Here is an example problem I have from my homework:

1) An urn contains 33 balls. Twelve are black, 11 are blue, 8 are silver, and 2 are gold. Round your answers to the following to 4 decimal places.

a) Find the probability that, if one ball is randomly removed from the urn, it is black.

b) Find the probability that, if two balls are randomly removed from the urn without replacement, they are both black.

c) If three balls are randomly removed without replacement, find the probability that they are all gold.

d) If two balls are removed without replacement, find the probability that one of them is blue.

Any help is appreciated. Thank you!

Re: MAT 142: An urn contains 33 balls. Twelve are black, 11

1) An urn contains 33 balls. Twelve are black, 11 are blue, 8 are silver, and 2 are gold. Round your answers to the following to 4 decimal places.

a) Find the probability that, if one ball is randomly removed from the urn, it is black.

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How many blacks are there?. How many balls total?.

Wouldn't it be 12/33?.

b) Find the probability that, if two balls are randomly removed from the urn without replacement, they are both black.

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If you draw one black, we have our first probability from part a. If you draw another black then you have 1 less black and 1 less ball total because of the first draw. (12/33)(11/32)

c) If three balls are randomly removed without replacement, find the probability that they are all gold.

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Tricky, be careful. You should see this right off. How many golds are in the bag?. How many are they asking you to draw?.

d) If two balls are removed without replacement, find the probability that one of them is blue.

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How many blues are in the bag?. 11

How many balls total?. 33

The chance of drawing a blue is 11/33

Since we're not replacing, the probability of drawing a non-blue next is everything else that's left after you draw the blue: 22/32

So, if you draw blue first, then the probability is (11/33)(22/32)

Suppose you drew a non-blue first, the probability would be 22/33.

Then draw the blue is 11/32

(22/33)(11/32).

So the proability would be (11/33)(22/32)+(22/33)(11/32)

i get it! thanks so much!