1. ## help combinations

two questions

1) a certain irrational number has a decimal expansion in which each digit is randomly chosen from the set (0,1,2,3,4,5,6,7,8,) find the probability that there is no pair of 9s in the first 100 pairs of digits.

2) the random variable s can take values 1,2,3........ and has a geometric distribution. it is given that p(s=2) = 0.2244 find the value of p(s=1) given that it is less than 0.5.

i think it starts p-p2 = 0.2244

thanks

2. Originally Posted by gracey
1) a certain irrational number has a decimal expansion in which each digit is randomly chosen from the set (0,1,2,3,4,5,6,7,8,) find the probability that there is no pair of 9s in the first 100 pairs of digits.
This is a great question , and I am sure my answer is wrong, but here it goes..

100 digits, 10 possibilities for each digit, we want no pairs of 9's

P(pair of 9's) = $\displaystyle (.1)^2 \Rightarrow .01$
P(non consecutive 9's) = 1 - P(pair of 9's) = .99

We need that 50 times over: $\displaystyle .99^{50} = .605$.

3. 1) This is rather funny. If you do not have a typo in your digit set, the probability of consecutive 9s quite obviously is zero.

2) Pr(1) = p
Pr(2) = q*p = 0.2244

q = 1-p

(1-p)*p = 0.2244 ==> p = 0.34 or p = 0.66 -- Which shall you pick?

4. Originally Posted by TKHunny
1) This is rather funny. If you do not have a typo in your digit set, the probability of consecutive 9s quite obviously is zero.
That is funny! I believe the OP meant to type a nine after that last comma!