Hi

Could you please explain to me how to do the following question?

"There are 12 beads in an urn, where 5 of them are blue, 4 are red and 3 are yellow. Beads with the same colour are identical. You pick out 9 beads randomly from the urn without replacement.

a) Find the probability that there are exactly 2 colours of beads chosen.

What I know: This means that you have to pick out the 5 blue and 4 red beads, meaning that each time, you can't pick out the yellow. This means that there is a probability of (9/12)*(8/11)*(7/10)... giving 9!4!/12!

b) Find the probability that there are exactly 3 blue beads chosen

This is where I get stuck. I simply have no idea what I am supposed to do here!

c) Suppose now that you randomly pick out 9 beads from the urn, but with replacement. Find the probability of observing exactly two colours of beads, red and yellow, in the 9 chosen beads. (Hint: Find the probability that no beads chosen are blue first.)

I am not entirely sure what to do here. The probability of not selecting a blue is 7/12. Do I just do (7/12)^9 as each time I am making the same selection?

Many thanks

Could you please explain to me how to do the following question?

"There are 12 beads in an urn, where 5 of them are blue, 4 are red and 3 are yellow. Beads with the same colour are identical. You pick out 9 beads randomly from the urn without replacement.

a) Find the probability that there are exactly 2 colours of beads chosen.

What I know: This means that you have to pick out the 5 blue and 4 red beads, meaning that each time, you can't pick out the yellow. This means that there is a probability of (9/12)*(8/11)*(7/10)... giving 9!4!/12!

b) Find the probability that there are exactly 3 blue beads chosen

This is where I get stuck. I simply have no idea what I am supposed to do here!

c) Suppose now that you randomly pick out 9 beads from the urn, but with replacement. Find the probability of observing exactly two colours of beads, red and yellow, in the 9 chosen beads. (Hint: Find the probability that no beads chosen are blue first.)

I am not entirely sure what to do here. The probability of not selecting a blue is 7/12. Do I just do (7/12)^9 as each time I am making the same selection?

Many thanks

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