Question

An urn contains 7 white balls and 4 red balls. Draw three balls from the urn without replacement. What us the probability that the first ball is read, the second white, and the third red?

Answer 1

Since each event is independent of the others, we can just find the probability of each individual event, then multiply them together

So we go to the first one, the first ball is red

Well, there are 4 red balls and 11 total balls, so that probability is `4/11`

Now the second, that the second ball is white

Since we aren't replacing, we now have 10 total balls, and still 7 white balls, so this probability is `7/10`

Now the last, that the third ball is red

One again, we aren't replacing, so we now have 9 total balls. Since we already took a red ball before, we now only have 3 red balls available, which gives `3/9`

Now the probability of the independent events happening together is just multiplying them together

`4/11 * 7/10 * 3/9`

Which is equal to `14/165`

And we are done.