There are 24 marbles in a bag eight are blue eight are white...

There are 24 marbles in a bag. Eight are blue, eight are white, and eight are gold. If the marbles are not replaced after the 1<sup>st</sup> draw, what is the probability of each of the following occurring in the given order? 23. P(white, blue) 24. P(white, blue, gold) 25. P(white or blue, gold) 26. P(gold | first draw was a white marble)

Transcript

00:01 All right, so we're given that there are a total 50 marbles that are either red or blue.

00:06 24 are marked with an a, and then six of those are red.

00:15 So six are red and have an a.

00:20 It says twice a many are blue and marked with a b.

00:26 So it's twice as many of those are blue and marked with a b.

00:29 So therefore, 12 are b or are blue.

00:36 And marked would it be.

00:41 So now we want to determine the probability is given.

00:46 So it says what is the probability that the marble is blue? okay.

00:55 So the probability that a marble is blue is just the 50.

01:08 But wait, we should step back.

01:10 Let's figure out the rest of them.

01:11 So if we have 24 that are marked a, then since the total of 50, 26 should be marked blue.

01:26 Let me be.

01:28 So if we have, let's adjust this, kind of make a table out of it.

01:35 So we're going to have 12 that are blue.

01:42 So therefore, added 26, 12, there should be 14 that are red.

01:52 And then out of the 6 here, there should be 18.

01:56 That are blue.

02:01 So in that case, now we can figure out the probabilities.

02:09 So we're asked, what is the probability for blue? well, that would just be the 12 plus 18 out of 50, so just 3 out of 5.

02:37 So about 0 .6.

02:42 The next one is the probability that the marble is marked with an a so probability of an a or there's 24 a's so therefore 24 out of 50 or just 0 .8 i mean 0 .48 next we asked the probability of the marble is not blue so if you're not blue then you're red so that's be 6 and 14 50 so that's 20 or 50 it's about 40%.

03:42 So then next one i ask is what is the probability that the marvel is marked to be or is blue? so marvel is blue.

03:56 I'm sorry, mark it to be or blue.

04:02 So in that case, the probability of being marked with a b is 26 out of 50 plus probability of being blue which is you forget it's 30 out of 50 and then we need to the minus the intersection the probability of being b or blue is here so 12 out of 50 so that's 56 minus 12 so 54 so 54 out of 50 so that's 88 percent next one is probability that the marble is marked with an a or is not red probably to a or not red so if it's not red, then it's blue.

05:11 It's a probability of a, which we found to be 30 over 50.

05:19 Plus, so not being red means you're blue.

05:23 The probability of being blue was, wait, i'm sorry...

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