Question

Two dice are rolled. Determine the probability of the following.Rolling an even number or a number greater than 7Submit Answer

Answer 1

The number on the dice from 1 to 6

Since we have 2 dice then the total out com will be 6 x 6 = 36

Let us find all outcomes

$\begin{gathered} (1,1),(1,2),(1,3),(1,4),(1,5),(1,6) \\ (2,1)(2,2),(2,3),(2,4),(2,5),(2,6) \\ (3,1),(3,2),(3,3),(3,4),(3,5),(3,6) \\ (4,1),(4,2),(4,3),(4,4),(4,5),(4,6) \\ (5,1),(5,2),(5,3),(5,4),(5,5),(5,6) \\ (6,1),(6,2),(6,3),(6,4),(6,5),(6,6) \end{gathered}$

Now we need to find the probability of an even number

The even numbers are the numbers that end by 0, 2, 4, 6, or 8

Then we will find all the outcomes that given an even number

$(1,2),(1,4),(1,6)$$(2,2),(2,4),(2,6)$$(3,2),(3,4),(3,6)$$(4,2),(4,4),(4,6)$$(5,2),(5,4),(5,6)$$(6,2),(6,4),(6,6)$

Then there are 18 even numbers, then the probability of an even number is

$\frac{18}{36}$

For a number greater than 7, The outcomes are

$\begin{gathered} (2,6),(4,6) \\ (4,4),(6,6),(6,2),(6,4), \end{gathered}$

There are 6 numbers greater than 7

The probability of a number greater than 7 is

$\frac{6}{36}$

For or we will add the 2 probabilities

$P(E\text{ or S>7\rparen=}\frac{18}{36}+\frac{6}{36}=\frac{24}{36}=\frac{2}{3}$

The answer is 24/36 or 2/3