What is the probability that in three consecutive rolls of two fair dice, a person gets a total of 7, followed by a total of 11, followed by a total of 7?

*Round to the nearest ten thousandth.

2 Answers
Jul 13, 2017

1/6*1/18*1/6 = 1/648

Explanation:

Let us consider the first case. We denote the probability of "getting a total of 7 in a throw of 2 fair dices" by P(A).

Now, there are 6 outcomes when we throw a dice, so the number of possible outcomes when we throw 2 dices at a time is

6*6=6^2=36

Now by observation, we get

1+6=7, 2+5=7, 3+4=7

They can interchange their position in 2! ways, so the number of all possible cases in favour of A is

3*2=6

Hence

P(A) = 6/36 =1/6

Let us consider the 2nd case. We denote the probability of "getting a total of 11 in a throw of 2 fair dices" by P(B).

Now, there are 6 outcomes when we throw a dice, so the number of possible outcomes when we throw 2 dices at a time is

6*6=6^2=36

Now by observation, we get

5+6=11

They can interchange their position in 2! ways, so the number of all possible cases in favour of B is

1*2=2

Hence

P(B) = 2/36 =1/18

Let us consider the 3rd case. It is the same as the first case, hence

P(C) = 6/36 =1/6

The required probability asked in the question is P(A nn B nn C).

The events A, B, C are independent, so

P(A nn B nn C) = P(A)*P(B)*P(C) = 1/6*1/18*1/6 = 1/648

Aug 4, 2017

1/648

Explanation:

A possibility space is a good way of showing the possible outcomes when two dice are rolled:

color(white)(........)ul(1" "2" "3" "4" "5" ")6

1:color(white)(.....)2" "3" "4" "5" "6" "color(red)(7)

2:color(white)(.....)3" "4" "5" "6" "color(red)(7)" "8

3:color(white)(.....)4" "5" "6" "color(red)(7)" "8" "9

4:color(white)(.....)5" "6" "color(red)(7)" "8" "9" "10

5:color(white)(.....)6" "color(red)(7)" "8" "9" "10" "color(blue)(11)

6:color(white)(.....)color(red)(7)" "8" "9" "10" "color(blue)(11)" "12

There are 6xx6= 36 possible outcomes

There are 6 ways of rolling 7 and 2 ways of rolling 11.

P(7,11,7) = 6/36 xx 2/36 xx 6/36

= 1/6 xx1/18 xx1/6

= 1/648