5LB Chapter 23 / ex 21 / p. 813

[antonia.vouraki]

Hi,

I would like to clarify the explanation given on the ex. 21, page 813, 5LB. I understand the answer. However, it is given an example of a slightly different question, i.e if we had to pick a specific number instead of just a red and a blue chip (as ex. 21 asks for).

So the explanation of the example of ex. 21 says: if it was asked to pick e.g. #3 from red and #3 from blue then the probability would be (1/6)*(1/6)=1/36. Keep in mind that we have 6 blue and 6 red chips on the same bag.

Although I understand the difference between ex. 21 and the above example, I was confused when I read the explanation of ex. 19 p. 813 which is asking exactly the same thing with what it was given as an example in ex. 21.

More specifically, ex. 19 asks what is the probability if we choose #3 from the black and #3 from the white chips. The number of black is 6 and the number of white is 6 as well. The explanation however of ex. 19 is different from the explanation for the example given in ex. 21.
The probability is (1/12)*(1/11)=1/132. Again, I understand this explanation as well.

However in order for ex. 19 and the example on ex.21 (not the actual question given) to make sense, I would think that on exercise 19 the black and white chips are in the same bag whereas on the example given on ex. 21 the red and blue chips are on separate piles thus in order to choose #3 for red and then #3 for blue we calculate (1/6)*(1/6)=1/36 instead of (1/12)*(1/11)=1/132.

Hope the above make senses. I would appreciate if you can confirm what is the reason of having different results for the same question (i.e. 1/36 vs 1/132). Am I correct to think that the difference is based on whether the chips are in 1 bag or in 2 separate bags or 2 separate piles?
Because the instructions given for both exercises (19 & 21) are exactly the same (i.e same bag, pick without replacement etc.)

Many thanks!!

[tommywallach]

Ignore the example given in that explanation for 21. It's incorrect.

Do you have a question beyond that?

-t

[antonia.vouraki]

Ok, thank you.

No I don't have any further questions. Since the example in ex 21 is incorrect, everything else makes sense.

Thank you for letting me know.

[tommywallach]

No problem. Apologies for that!