1. ## Dice and Doubles

Hey everyone,
Here's the question:

a)Two dice are thrown n times in succession. Compute the probability that a double six appears at least once. How large does n have to be for this probabablity to be at least 1/2?

b)Two dice are thrown n times in succession. Compute the probability that some double(be it 6's or 5's...) appears at least once. How large does n have to be for this probability to be at least 1/2?

ok, so I know that the probability for double sixes would be 1/6 * 1/6 = 1/36. I definitly don't know how to figure out how many throws you would need for the probability to be 1/2.

Thanks!

2. Originally Posted by kelli_rie
Hey everyone,
Here's the question:

a)Two dice are thrown n times in succession. Compute the probability that a double six appears at least once. How large does n have to be for this probabablity to be at least 1/2?

[snip]
(a) Let X be the random variable number of double sixes.

X ~ Binomial(n, p = 1/36).

(i) $\Pr(X \geq 1) = 1 - \Pr(X = 0) = 1 - \left( \frac{35}{36}\right)^n$.

(ii) You require the smallest integer value of n such that $\Pr(X \geq 1) \geq \frac{1}{2} \Rightarrow \left( \frac{35}{36}\right)^n \leq \frac{1}{2}$.

Trial and error is as good a way as any for solving for n.

3. Originally Posted by kelli_rie
[snip]
b)Two dice are thrown n times in succession. Compute the probability that some double(be it 6's or 5's...) appears at least once. How large does n have to be for this probability to be at least 1/2?

[snip]
Let Y be the random variable number of doubles.

Y ~ Binomial(n, p = .....)

You should be able to calculate the value of p (the probability of getting a double in a single throw). Now model your solution on the solution to (a).