Question

In the game of Monopoly, a player is sent to jail if he or she rolls doubles with a pair of dice 3 times in a row.What is the probability of rolling doubles on a single turn? (Enter your probability as a fraction.) _______What is the probability of rolling doubles 3 times in succession? (Enter your probability as a fraction.) _______

Answer 1

The probability of rolling doubles on a single turn is the number of favorable cases over the number of total cases, the favorable cases are those when you get a double, the number of total cases is the number of total possible outcomes.

Now, the number of total possible outcomes is

`6*6=36.`

The number of favorable cases is

`6.`

Therefore, the probability of rolling doubles is:

`(6)/(36)=(1)/(6)\text{.}`

Now, the probability of rolling double 3 times in succession is the product of rolling a double in a single turn, therefore:

`P=(1)/(6)*(1)/(6)*(1)/(6)=(1)/(216).`

Answer:

The probability of rolling doubles on a single turn is:

`(1)/(6)\text{.}`

The probability of rolling doubles 3 times in succession is:

`(1)/(216)\text{.}`