Question

When rolling a die what is the probability of getting a number greater than 2 and an even number

Answer 1

Let's find the probability of getting a number greater than 2 and an even number when rolling a die.

Where:

Number of possible outcomes = 6

Numbers greater than 2 = 3, 4, 5, 6 = 4 numbers

Even numbers in a die = 2, 4, 6 = 3 even numbers.

Here, we have to find:

P(greater than 2) x P(even)

We have:

`\begin{gathered} P(\text{greater than 2) = }\frac{\text{ numbers greater than 2}}{total\text{ outcome}}=(4)/(6)=(2)/(3) \\ \\ P(\text{even)}=\frac{\text{ number of even numbers}}{total\text{ outcome}}=(3)/(6)=(1)/(2) \end{gathered}`

Hence, to find probability of getting a number greater than 2 and an even number​, we have:

`P(\text{greater than 2) }* P(even)=(2)/(3)*(1)/(2)=(2*1)/(3*2)=(2)/(6)=(1)/(3)`

Therefore, the probability of getting a number greater than 2 and an even number is 1/3

ANSWER:

`(1)/(3)`