Inside a bag, there are three green balls,

two red balls, and four yellow balls. Two balls are randomly drawn without replacement. Calculate the probability of drawing one red

ball and one yellow ball. So, let’s consider, : what’s What’s the probability

of drawing one red ball and one yellow ball? So, the probability of drawing one red and

one yellow. Well, there are two different ways in which

we could draw a red ball and a yellow ball. We could draw a red ball first, and then on

the second ball we could draw a yellow ball. Or, we could draw a yellow ball first and

then a red ball. So, in other words, this probability is going

to be the sum of drawing red then yellow and drawing yellow then red. And, in order to find out these two probabilities,

let’s draw a probability tree diagram. So, there are actually three probabilities

here. There are three possible outcomes that we

have to consider. So, on the first draw we could get a green

ball or we could get a red ball or we could get a yellow ball. So, because of that we’re going to have three

branches coming out of our probability tree. And here we’re told there are three green

balls, and how many balls we’ve got all up? We’ve got three, two, four, so that’s nine

balls all up. So, the probability of drawing a green ball

on the first draw is going to be 3 over 9. Now, there are two red balls, so the probability

of drawing a red ball on the first draw is going to be 2 over 9. And the probability of drawing a yellow ball,

there are four yellow balls, so that’s gonna be 4 over 9. OK, once we’ve drawn the green ball, there

are still some green balls left in the bag and still some red balls and still some yellow

balls. So, from this green ball, we now have another

three branches coming out. We could draw a green ball, a red ball, or

yellow ball. Now, what’s the probability of drawing a green

ball if we’ve already drawn a green ball in our first draw? Let’s quickly draw a bag and imagine that

we have a bunch of balls here. Imagine that we have three green balls and

we have two red balls and we also have four yellow balls. Well, if we on the first draw have already

drawn out a green ball, on our second draw we’re going to have one fewer green ball than

we had before. Which means that the probability of now drawing

a green ball is going to be—there only two green balls left in this bag and all up there

are only eight balls—so the probability of drawing a green ball considering that these

are drawn without replacement is going to be 2 over 8. What about the probability of drawing a red

ball? Well, there are two red balls here and eight

balls all up, so that’s also going to be a probability of 2 over 8. So, the probability that we draw a yellow

ball, given that we’ve drawn a green ball on our first draw, is going to be one, two,

three, four—there are four yellow balls and eight balls all up, so that’s going to

be 4 over 8. Now, if we are to repeat that process, we

have to repeat that process a couple more times in order to fill out this probability

tree. So, here for red we’ve got three possibilities. We could have green, red, and yellow. So, remember this is the outcome that we’ve

got a red ball on the first draw. So, if we had a red ball on the first draw,

let’s quickly draw our balls again, and have three green and four yellow, so here we’re

imagining the first draw we reach in and we draw a red ball. So, what’s the probability from this bag now

of drawing a green ball? Well, there are three green balls and eight

balls all up, so the probability is 3 over 8. What about the probability of drawing a red

ball? That’s going to be 1 over 8. And a yellow ball? That’s going to be 4 over 8. OK, this is going well. We’ve just got three more branches to go. So, here imagine that we draw a yellow ball

on our first draw. Well, we could draw a green, a red, or a yellow

on a second. Again, if we’ve got our bag, imagine we’ve

still got three green, got two red, and we’ve got a few yellow balls here. We’ve got four yellow. So, imagine that we draw out a yellow ball

on the first draw. So, we’ve got one fewer yellow ball than

the first draw, . so So here what’s the probability of getting a green ball? Well, there are eight balls, and three of

them are green, so this is going to be 3 over 8. Here, the probability of getting a red ball,

that’s going to be 2 over 8. And the probability of getting a yellow ball,

that’s going to be 3 over 8. So, we’re interested in two outcomes, red

yellow and yellow red. So, red yellow, that corresponds to red on

the first ball, yellow on the second ball. So, red yellow is here. So, the probability of getting red yellow. S, so, red on the first, yellow on the second,

is going to be 2 over 9 times 4 over 8. So, the probability associated with first

branch multiplied by the probability associated with the second branch. So, 2 over 9 times 4 over 8. Well, 4 over 8 is the same as a half, so that’s

going to be 2 over 9 times a half. We’ve got a common factor of 2, so this is

going to be 1 over 9 multiplied by 1 over 1. That’s just going to be 1 over 9. So, that’s the probability of drawing a red

on the first draw and a yellow ball on the second draw. What about yellow red? So, it’s yellow on the first draw, red on

the second draw. So, the probability here of yellow red, we’re

going to do something very similar. Going toThen you get 4 over 9 times 2 over

8. Four over 9 times 2 over 8. Two over 8 is a quarter, so it’s going to

be 4 over 9 times a quarter. And here we’ve got a common factor again of

4, so this is going to be 1 over 9. That’s 1 over 1. So, this is going to be 1 over 9 as well. So, here, we’ve got the probability of one

red and one yellow is going to be 1 over 9, the probability of red and yellow. Plus the probability of yellow red, that’s

going to be 1 over 9 again, so that’s going to be 2 over 9.

Thanks, you've helped a lot.

struggled for tree diagrams, it was great to see how everything made more sense how you drew out the bag and crossed out the red green and yellow ball. Keep up the great work

Hi Mark! Interested in adding transcripts to your videos. Would you please email me at [email protected]? Thanks!

But it is written that 2 balls r drawn randomly

Wouldnt this solution be if one is drawn randomly