Normal Distribution

SBS261P SG

I came across this question and still cannot resolve the 2 arguments, hope that someone can enlighten me here!

A duck shop sells duck that have weight normally distributed with mean weight 2.7kg and variance 0.424.

wee_ws SG

Hi,

In your first method, you considered the multiplication principle.

In your second method, you considered the mutual exclusion principle (where you make the claim that one duck may cost $11 or more).

If the most expensive duck is below $11, certainly all others must cost less. Therefore, it is logical to consider method 1 in that all 4 ducks cost below $11.

In addition, it is utypical to encounter a probability that is constant regardless of the event (e.g. number of ducks).

Thanks.

Cheers,
Wen Shih

SBS261P SG

my question is, isn’t the two cases the same thing? means I’m overcounting the second case? but where is the overcounting?

Mad Hat SG

Hi SBS261P

In the second case, when you say P(1 duck cost ≥ 11), the real meaning is P(At least 1 duck cost ≥ 11). This is not the same as P(4X ≥11).

SBS261P SG

4X is defined as the price of a duck. the argument put forward is since there is 1 duck already, it doesn’t matter how much the other ducks cost (by pigeonhole principle). sounds intuitively correct bt inherently wrong, but I can’t find counterexample to disprove this working.

I thought of the following to refute this working:

-are we considering order of ducks when we do this?
-is there conditional probability?

the 2nd working was put forward by one of my students and I can’t seem to find a way to explain it is wrong… =(

wee_ws SG

Hi,

Mutual exclusion does not apply for this problem, period. That is all the student should be advised on.

Probabilistic reasoning is hard and abstract at times. Use logic to appeal to the student instead.

Btw, the Pigeonhole Principle is not assessed in H2 Mathematics, in case the problem originated from that.

Thanks.

Cheers,
Wen Shih

TenSaru SG

1 - P(1 duck >11) is the same as P(1 duck < 11) but that doesn't mean that it is the most expensive duck...

So if 1 duck is >11 that means the rest of the duck do not need to be considered

but if 1 duck < 11 there is still a chance that the other 3 ducks can have 1 that is >11

Konnichiwa SG

A duck shop sells duck that have weight normally distributed with mean weight 2.7kg and variance 0.424.Given that 1 kg of duck costs $4, find the probability that out of 4 randomly chosen ducks, the most expensive duck will be below $11.