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# Probability Q Watch

1. Hi guys,

On the above question I got the probability the prince is not disturbed = 6/10. Can anyone confirm if this is right/wrong??

Thanks for any help in advance.
2. (Original post by hmark101)

Hi guys,

On the above question I got the probability the prince is not disturbed = 6/10. Can anyone confirm if this is right/wrong??

Thanks for any help in advance.
Assuming that he has undisturbed sleep if there is no pea present, and that with the 8 mattresses, he has 2 in 5 nights undisturbed sleep when there is a pea present (the wording of the last part seems ambigous to me, but only really makes sense with this interpretation), then yes, 6/10.
3. (Original post by ghostwalker)
Assuming that he has undisturbed sleep if there is no pea present, and that with the 8 mattresses, he has 2 in 5 nights undisturbed sleep when there is a pea present (the wording of the last part seems ambigous to me, but only really makes sense with this interpretation), then yes, 6/10.
Thanks.

I am having trouble working out the expectation of the number of mattresses for the last part. Using Baye's formula (which we were asked to prove in part a), I have values for P(chose i mattresses | sleep not disturbed), for i = 6, 7, 8.

Do you know how I can use that (if needed at all) to work out expectation? It's not in my notes anywhere.

Many thanks.
4. (Original post by hmark101)
Thanks.

I am having trouble working out the expectation of the number of mattresses for the last part. Using Baye's formula (which we were asked to prove in part a), I have values for P(chose i mattresses | sleep not disturbed), for i = 6, 7, 8.

Do you know how I can use that (if needed at all) to work out expectation? It's not in my notes anywhere.

Many thanks.
Again the wording seems strange for this last past. I would interpret it as the most likely number of mattresses, rather than working out any expectation. In which case I'd say 8.

Edit: I see this is from the Cambridge Tripos, so my simplistic thinking may be too simplistic.

In which case expectation would be sum 6 to 8, #mattresses times P(chose i mattresses | sleep not disturbed)

But it doesn't seem right to me to be looking for that sort of answer.

I think you may need a Cambridge grad on this one.

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