1. The Newton-Pepys problem: Assume the following problem only involves fair, si

ID: 3204374 • Letter: 1

Question

1. The Newton-Pepys problem: Assume the following problem only involves fair, six- sided dice.

(a)

i. What is the total number of possible outcomes rolled when rolling six dice?

ii. How many of these possible outcomes have no “6”s?

iii. Use the above two answers to calculate the probability that, when rolling six dice, at least one “6” is rolled.

(b)

i. What is the total number of possible sequences rolled when rolling 12 dice?

ii. How many of these possible outcomes have either no “6”s or exactly one “6”?

iii. Use the above two answers to calculate the probability that, when rolling twelve dice, at least two “6”’s are rolled.

(c)

i. What is the total number of possible sequences rolled when rolling 18 dice?

ii. How many of these possible outcomes have no “6”s, exactly one “6”, or exactly two “6”s?

iii. Use the above two answers to calculate the probability that, when rolling eighteen dice, at least three “6”s are rolled.

Solution:-

(i)The total number of possible outcomes rolled when rolling six dice = 66 = 46,656.

(ii) The possible outcomes have no “6”s is 15,625

For having no 6 we have different outcomes:-

Total number of outcomes = 56 = 15,625

(iii) The probability that, when rolling six dice, at least one “6” is rolled is 0.16667.

For having 6 atleast we have different outcomes:-

(6, _, _, _, _, _ )

Total number of outcomes = 65 = 7,776

The total number of possible outcomes rolled when rolling six dice = 66 = 46,656.

The probability that, when rolling six dice, at least one “6” is rolled = 7776 / 46656 = 0.16667.

(i)The total number of possible outcomes rolled when rolling 12 dice = 612 = 2,176,782,336

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