Six different colored dice are rolled. Of interest is the number of dice that show a "5."

Question

Six different colored dice are rolled. Of interest is the number of dice that show a "5."

Part (a)

In words, define the Random Variable X.

1. how many dice are rolled
2. the color of the dice
3.  how many dice show a "5"
4. the outcome of the roll of the dice

Part (b)

List the values that X may take on.

1. X = 5
2. X = one, two, three, four, five, six    
3. X = two, four, six
4. X = zero, one, two, three, four, five, six

Part (c)

Give the distribution of X. (Enter the probability as a fraction.)

x~_____(_____,_____)

Part (d)

On average, how many dice would you expect to show a "5"?

1.  _____die (dice)

Part (e)

1. Find the probability that all six dice show a "5." (Round your answer to five decimal places.)

Answer 1

6 dice probably have the 3 primary colors & 3 secondary colors: red, blue & yellow, and orange, purple & green.

although black & white are possible, invisible colors most unlikely: ultraviolet & infrared

each die has 6 possible outcomes, 1 through 6. there is no zero die outcomes, just 1,2,3,4,5 or 6.

a 5 has 1/6 chance on each die. one way to get a five, divided by total number of possible outcomes

For all 6 to have 5's, the probability is (1/6)^5 = 1/6 x 1/6 x 1/6 x 1/6 x 1/6 x 1/6 = about 0.00002