Two balls are chosen randomly from a jar containing 8 red 4...

Two balls are chosen randomly from a jar containing 8 red, 4 blue, and 2 yellow balls. Suppose that we win $2 for each blue ball selected and we lose $1 for each red ball selected. Let X denote our winnings. What are the possible values of X, and what are the probabilities associated with each value

Transcript

00:03 Hello, so here we've been giving 8 red, 8 red, 4 blue and 2 yellow.

00:13 So we're going to try and look at all the possible probabilities, first all the possible values of x and then corresponding probabilities.

00:23 So you've been told that if you pick a blue ball, you get 2 dollars, if you pick a red one, you can lose 1 dollar.

00:32 Let's look at all the possible values of x.

00:35 So since you are drawing two balls, so many things are possible.

00:42 So let's look at all the possibilities.

00:45 So for example, if you are drawing two balls and that you draw four blue, two blue balls, you get $2.

01:01 So you get $2 for you.

01:08 So if you draw two blue balls, you get $2 for each.

01:13 That gives you four, right? and the corresponding probability is 4 combination 2.

01:24 That's 2 out of the 4.

01:26 Divided by the total, which is 410 combination 2, is going to be 6 over 91.

01:40 So this is when you draw 2 blue balls.

01:44 You get $4.

01:47 As the first scenario, let's look at a second scenario.

01:53 So x would be equal to...

01:58 2 plus 0 what does this mean so this equal to 2 so what this means is you get only $2 to me that you draw one blue ball okay because if you draw one blue ball you get two dollars right so if you draw only one blue ball and then you draw a yellow ball because a yellow ball you don't have any information on yellow ball so we're assuming that nothing happens okay so this is uh so let me just right this right this is here.

02:38 This is two blue balls.

02:46 This one is one blue ball plus one yellow...

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