Thread: Probability - Coins

I need a wee help with this little thing:

A fair coin is being thrown until H comes up for the first time. Let N be the number of times needed for H to turn up. If N=n, we throw n fair dices. Let S be the sum of the numbers turning up on the N dices.

a. find the probability that N=1 if you know that S=4, and the probability that S=6 if you know that N is an even number.

b.Show that the probability that the biggest number the appears on one of the dices is smaller or equal to K is K/12-k ( K is between 1 to 6 )

c.Find the probability that the biggest number that apears on at least one of the dices is K.

I have tried to solve "a" with Bayes's Theorem, but I don't know how to calculate P(S=4)....

cheers
( and sorry about my english...)

Originally Posted by WeeG

I need a wee help with this little thing:

A fair coin is being thrown until H comes up for the first time. Let N be the number of times needed for H to turn up. If N=n, we throw n fair dices. Let S be the sum of the numbers turning up on the N dices.

a. find the probability that N=1 if you know that S=4, and the probability that S=6 if you know that N is an even number.

Use Baye's Theorem
, condition on N in the denominator to get



Now P(S=4|N=k) is non-zero only for N = 1, 2, 3, 4. Thus the denominator d becomes


Finally

For the next part we know that N must be 2, 4 or 6.

cheers