Two dice are rolled. Determine the probability of the following: rolling a 6 or doubles

Answer as an exact fraction = 5/18

Answer as an approximate decimal = 0.2778

Answer as an approximate percentage = 27.78%

Explanation:

x = result of the first die

y = result of the second die

(x,y) paired together shows the results of both dice at the same time.

Something like (x,y) = (4,2) means we got 4 on the first die and 2 on the second die.

Let's list the ways of rolling a 6

There are 5 ways to roll a 6. Each pair listed has the property x+y = 6.

List all the ways of getting doubles

There are 6 ways to roll doubles. Each pair mentioned has x = y.

We have 5+6 = 11 items listed above. However, there are only 10 unique pairs though because (3,3) was listed twice. So we could say 5+6-1 = 11-1 = 10.

This is out of 6*6 = 36 different ways to roll the two dice. The probability is therefore 10/36 = 5/18.

Using a calculator, 5/18 = 0.2778 = 27.78%

2^y = ln 5, or   y(ln 2) = ln 5.   solving for y,   y = (ln 5) / (ln 2).   y=5

step-by-step explanation: