Question

Six different colored dice are rolled. Of interest is the number of dice that show a "3." (D) On average, how many dice would you expect to show a "3"? (E) Find the probability that all six dice show a "3." (Round your answer to five decimal places.) (F) Is it more likely that three or that four dice will show a "3"?

Answer 1

Given data:

6 different coloured dice are rolled.

n = 6

Of interest is the number of dice that show a "3"

p = 3/6 = 1/2

To calculate:  

D) On average, how many dice would you expect to show a "3"?

(E) Find the probability that all six dice show a "3."

(F) Is it more likely that three or that four dice will show a "3"?

Now,  

D) Out of 6 dice, 6 dice shows 3

So Average = E(x) = n × p

= 6 × 1/2

= 3

Therefore on average 3 dice would expect to show a "3"

E) The probability that all 6 dice shows a "3"

P = (3/6) ⁶ = (1/2) ⁶ = 0.01562

Therefore the probability that all 6 dice shows a "3" is 0.01562

F) Half of the 6 dice shows "3" .

So 6/2 = 3

Therefore 3 dice are more likely to show a "3"