1. ## Probability-Sequences of Events

Suppose you roll a fair six-sided die repeatedly until the first time you roll a number that you have rolled before.
a)For each r=1,2,…calculate the probability pr that you roll exactly r times.
b)Without calculation, write down the value of p1 + p2 + . . . +p10. Explain.
c)Check that your calculated values of pr have this value for their sum.

2. Originally Posted by Yan
Suppose you roll a fair six-sided die repeatedly until the first time you roll a number that you have rolled before.
a)For each r=1,2,…calculate the probability pr that you roll exactly r times.
b)Without calculation, write down the value of p1 + p2 + . . . +p10. Explain.
c)Check that your calculated values of pr have this value for their sum.
a) Let p(n) denote the probability of exactly n throwns before a repeat is obtained:

p(1)=0
p(2)=(1-p(1)(1/6)
p(3)=(1-p(2)-p(1))(2/6)

p(n)=(1-p(n-1)-p(n-2)-..-p(1))[(n-1)/6]

n=1, .. ,6 and p(n)=0 for n>6

RonL

3. how to answer the part b and c?

4. Originally Posted by Yan
how to answer the part b and c?
For part b you have to think about what the question means, then when you have part b part c follows just be using the result of a and comparing the sum with what you will know from thinking about what b is asking for.

RonL

5. I don't get what is this question mean, can you explain to me!!
Thanks

6. Originally Posted by Yan
I don't get what is this question mean, can you explain to me!!
Thanks

If I throw 10 six sided dice what is the probability that they all show different faces.

RonL