Answer:
Step-by-step explanation:
Six dice (each of a different color) are rolled. Since the number of times the 6 dice were rolled isn't stated, take it to be 1.
Hence, 6 dice are rolled at once for this experiment.
Of interest is the number of dice that show a "one". In other words, the variable in question (X) is:
The number of dots that show on the upward face of the rolled dice.
The values that X may take on are:
1 2 3 4 5 6
On average, how many dice would you expect to show a one?
One die.
How is this gotten? By finding the probability that a one or one dot appears when the 6 dice are rolled at once. Since there are 6 dice in number, and each die has the same 6 faces containing dots, the probability of getting a one is 1/6. In this case, one out of 6 dice is expected to show one dot.
Find the probability that all six dice show a dot in just one toss.
Logically, this probability is going to be very small! It is almost impossible for all 6 dice to land on the same face in just a single toss. In other words, expect many decimal places in the probability figure.
1/6 divided by 6 = 0.167/6 = 0.028 approximated to three decimal places.
This would also represent the probability that 2 dots, 3 dots, or any other number of dots appears on all dice in one toss!
Is it more likely (in this experiment) that 3 or 4 dice will show a one (a single dot)?
The answer is yes! It is more likely that 3 or 4 dice (instead of all 6) will show a one or will show the same number of dots.
Kudos!
, we have for 
the Taylor series expansion about 0 as
with 
, so that the series is equivalent to
, we have
