Question

When playing many games, players must roll a pair of dice and find the sum of the two numbers rolled. With two dice, there are 11 possible sums ranging from 2 through 12. What is the probability that a player will roll a sum of 11 on his first roll of two dice? Express your answer as a common fraction.

Answer 1

Answer:

$Probability = \frac{1}{18}$

Step-by-step explanation:

Given

$Dice = 2$

Required

Probability of getting sum of 11

First, we need to list out the sample space;

Represent the first dice with S1 and the second with S2

$S_1 = \{1,2,3,4,5,6\}$

$S_2 = \{1,2,3,4,5,6\}$

Represent the Sum of the outcome with S

So, the new sample space is the sum of outcome of S1 and S2

So, S is as follows:

$S = \{2,3,4,5,6,7,3,4,5,6,7,8,4,5,6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12\}$

Represent the number of sample space with n(S)

$n(S) = 36$

To determine the probability of outcome of 11, we need to list out the number of outcomes of 11.

Represent this with n(11)

From the sample space above,

$n(11) = 2$

The required probability is then calculated as thus:

$Probability = \frac{n(11)}{n(S)}$

$Probability = \frac{2}{36}$

Simplify to the least term

$Probability = \frac{1}{18}$