4 in a box of marbles there are 16 yellow marbles 20 blue...

In a box of marbles, there are 16 yellow marbles, 20 blue marbles, 12 red marbles, and 12 black marbles. (Questions a, b, and c are mutually exclusive). a. What is the probability if I want to take 3 marbles in a row without returning the marbles after the first pick, and the results from the first to the third pick are blue, yellow, and black? b. If I only want to pick 1 marble, what is the probability that my pick is blue or red? c. What is the probability if I want to take 2 marbles in a row with returning the marble from the first pick, and the results of the first and second pick are black and yellow?

Transcript

00:01 Okay, in this problem we have 16 yellow, 20 blue, 12 red, and 12 black marbles.

00:05 And we're saying, what's the probability of these different options? well, the first thing we need to do is find the total.

00:10 So 16 plus 12, plus 12, plus 20.

00:14 Well, 16 plus 12 plus 12 is going to be, well, 10, 20, 30, 40, plus 20 is going to be 60.

00:21 So it's going to be 60 marbles total.

00:24 All right? so my probabilities are all going to have 60 as the denominator at first.

00:28 So the probability if i want to take three marbles in a row without returning the marbles after the first pick, and the results when the first to the third are blue and yellow and black.

00:37 Well, how many blues do we have? we have 20.

00:40 So the probability of drawing a blue first is 20 out of 60, right? then we're going to multiply that times the probability of after getting a blue, we want to get a yellow.

00:50 Well, how many yellows are there? well, there's 16.

00:52 But now there's no longer 60.

00:54 There's only 59 marbles to choose from because we're not putting them back.

00:59 All right.

00:59 And then, so it says blue, then yellow, and then black.

01:02 Well, how many blacks are there? there's 12 out of now 58.

01:06 12 out of 58.

01:07 So i can immediately say, okay, this goes down to one -thirds.

01:12 This is one -third.

01:14 Right.

01:15 And then we can say, well, does three go into 12? yeah, three goes into 12 four times.

01:20 Right.

01:20 So i have my three just cancels out now.

01:23 And now i can say it, well, does four go into 58? yeah.

01:26 So they're both even.

01:27 So i can say that that's two.

01:29 58 is what a 58 divided by 2 is going to be 20 29 yeah so two out of 29 all right and i think that that's going to be the last thing i can do because none of these are even so we'll have 32 divided by 59 times 29 i don't know what that is so 59 times 29 i want to put that in my calculator and that's going to be 1 ,711 so 1711 and that's my answer to my first one all right now and the second one, if i only want to pick one marble, what's the probability that my pick is blue or red? well, they're mutually exclusive.

02:06 I can pick one or the other...

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