At least once Clarification

• Jan 7th 2010, 11:23 AM
IDontunderstand
At least once Clarification
A roulette wheel in Europe has 37 compartments numbered 0,1,2,...,36. Find the probability that the number 29 will come up at least once in each case.

Two successive spins the answer says .0533

I want to say that (1/37)*(1/37)

That is the probability that 29 comes up both times and multiply between them.

If I add I get that answer, do I add because it says at least?

Thanks for the help
• Jan 7th 2010, 11:31 AM
artvandalay11
you need to use the binomial distribution...

Since it says at least once, that means we need 29 to come up exactly once or exactly 2, which is where binomial comes in handy

The number of trials will be 2 and the probability of success will be $\displaystyle \frac{1}{37}$

can you answer it now?
• Jan 7th 2010, 11:50 AM
Plato
Here is another way. What is $\displaystyle 1-\left(\frac{36}{37}\right)^2=?$
Why does that work?
• Jan 7th 2010, 02:33 PM
IDontunderstand
Would that be due to since the probability has to equal one since probability that it wont happen is (36/37) and I want it twice I can just square it
• Jan 7th 2010, 02:39 PM
Plato
Quote:

Originally Posted by IDontunderstand
Would that be due to since the probability has to equal one since probability that it wont happen is (36/37) and I want it twice I can just square it

At least one is the oppsite of none.
The probability of not getting a 28 twice is $\displaystyle \left(\frac{36}{37}\right)^2$.
• Jan 7th 2010, 02:47 PM
IDontunderstand
Quote:

Originally Posted by artvandalay11
you need to use the binomial distribution...

Since it says at least once, that means we need 29 to come up exactly once or exactly 2, which is where binomial comes in handy

The number of trials will be 2 and the probability of success will be $\displaystyle \frac{1}{37}$

can you answer it now?

so then I can say nCr (p)^r (q)^n-r

so: 37 C 1 (1/37)^1 (36/37)^36 + 37 C 2 (1/37)^2 (36/37)^35 should give me the correct answer then but when I do this it does not work
• Jan 7th 2010, 03:02 PM
Plato
Quote:

Originally Posted by IDontunderstand
so then I can say nCr (p)^r (q)^n-r

so: 37 C 1 (1/37)^1 (36/37)^36 + 37 C 2 (1/37)^2 (36/37)^35 should give me the correct answer then but when I do this it does not work

Yes it does. Caculate this: $\displaystyle \left(\frac{1}{37}\right)\left(\frac{36}{37}\right )+\left(\frac{36}{37}\right)\left(\frac{1}{37}\rig ht)+\left(\frac{1}{37}\right)^2$.