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:
[tex]\begin{gathered} P(\text{greater than 2) = }\frac{\text{ numbers greater than 2}}{total\text{ outcome}}=\frac{4}{6}=\frac{2}{3} \\ \\ P(\text{even)}=\frac{\text{ number of even numbers}}{total\text{ outcome}}=\frac{3}{6}=\frac{1}{2} \end{gathered}[/tex]Hence, to find probability of getting a number greater than 2 and an even number​, we have:
[tex]P(\text{greater than 2) }\times P(even)=\frac{2}{3}\times\frac{1}{2}=\frac{2\times1}{3\times2}=\frac{2}{6}=\frac{1}{3}[/tex]Therefore, the probability of getting a number greater than 2 and an even number is 1/3
ANSWER:
[tex]\frac{1}{3}[/tex]
