"rolling dice" probability question

[amymontg]

working on finite math for a college course, using standard deviations, mean, find probability of randomly selected blah blah. We are using a z-score chart. This problem has me stumped:
"A fair pair of dice is rolled 92 times. find the probability that the same point comes up on both dice at least 16 times."
so I know that n = 92.
There are only 6 ways the same point can come up on both dice, so would p = 1/6?
x is greater than/= to 16.

Thanks! math not my strongest.

 

[tkhunny]

You are missing something.

Technically this is a multinomial experiment. 1-6, each with probability 1/6.

Thankfully, we can simplfy by thinking of only one, making it a binomial experiment. p = 1/6, vs. q = 5/6, with n = 92

However, as we REALLY don't want to calculate all teh probabilities for ">16", there is a better way. Let's assume that 92 is big enough that a normal approximation is sufficient. This gives 92 * (1/6) = Mean and 92 * (1/6) * (5/6) = Variance. You should be able to use your z-score from there.

One last thing, you should ponder the implications of thinking on only one element. Are you tempted to multiply by 6? Discuss. Careful.