Year 12s: what will be the first way you research your future options? >>

Stats 2 Discrete probability distributions

Hi,

I'm a little confused with a question I've got on the above topic.

A bag with 5 blue counters and 4 red counters. 2 are picked without replacement, find in the form of a table, the probability distribution for the discrete random variable X, the number of blue counters picked.

I'm finding it confusing because 2 are picked. For example, are the picked together, simultaneously? Is one picked after the other, in so doing decreasing the denominator from 9 to 8?

I would have thought that picking 0 blue counters, would be the same as picking 2 red counters. There are 4 red counters, and 9 in total, so I thought that would be 4/9, but in the table for the answer, the result for picking 0 blue is 1/6.

Having failed to understand it I just tried to use the equation, but that didn't work either, obviously misunderstanding what values to sub in where.

Would anyone be able to help?

Thanks
Marc

(edited 10 years ago)

Reply 1

ghostwalker

Original post by marcsaccount

Hi,

I'm a little confused with a question I've got on the above topic.

A bag with 5 blue counters and 4 red counters. 2 are picked without replacement, find in the form of a table, the probability distribution for the discrete random variable X, the number of blue counters picked.

I'm finding it confusing because 2 are picked. For example, are the picked together, simultaneously? Is one picked after the other, in so doing decreasing the denominator from 9 to 8?

I would treat it as one after the other. Although treating them simultaneously would give the same answer, it's more complicated as you would have to distingush between "1 red and 1 blue" and "1 blue and 1 red", which isn't obvious when you choose two together. Even if you choose two together, you look at one first, and then the other, so it's still ordered really.

I would have thought that picking 0 blue counters, would be the same as picking 2 red counters. There are 4 red counters, and 9 in total, so I thought that would be 4/9, but in the table for the answer, the result for picking 0 blue is 1/6.

Yes, 4/9 for the first red, and then 3/8 for the second, and multiply.

Reply 2

marcsaccount

Original post by ghostwalker

I would treat it as one after the other. Although treating them simultaneously would give the same answer, it's more complicated as you would have to distingush between "1 red and 1 blue" and "1 blue and 1 red", which isn't obvious when you choose two together. Even if you choose two together, you look at one first, and then the other, so it's still ordered really.

Yes, 4/9 for the first red, and then 3/8 for the second, and multiply.