Three fair dice are rolled at once. Let X denote the number of dice that land with the same number of dots on top as at least one other die. The probability distribution for X is x 0 u 3 P ( x ) p 15 36 1 36 Find the missing value u of X. Find the missing probability p. Compute the mean of X. Compute the standard deviation of X.

can be any of 0, 2, or 3, which is to say the value of the dice are all different, 2 of them match, or all 3 are the same. So .

For any probability density, the probabilities of all possible outcomes must sum to 1. This means

The mean/expectation of is

The variance of is

where the second moment is

Then the standard deviation is the square root of the variance:

answer: 10 turtles

step-by-step explanation: as turtles have four legs so 4.10=40 therefore birds are 4 which sue counted