Question

A single six sided dice is rolled. Find the probability of rolling an even number or a number less than four

Answer 1

Answer: $Pr(even\text{ number or less number than 4\rparen = 5/6}$

Explanation:

Given:

A single 6-sided die is rolled

To find:

the probability of rolling an even number or a number less than four

To determine the probability, we will find the pr(rolling an even number) and the pr(rolling a number less than 4)

pr(rolling an even number) = number of even numbers/total numbers

even number = {2, 4, 6}

Total of even number = 3

Total numbers = 6

$Pr(even\text{ number\rparen = }\frac{3}{6}$

Pr(rolling a number less than 4) = numbers less than 4/total numbers

numbers less than 4 = {1, 2, 3}

Total of the numbers less than 4 = 3

Total = 6

$Pr(less\text{ than 4\rparen = }\frac{3}{6}$

From both numbers listed, we find that 2 is common in both probabilities. We will deduct the intersection

Pr(of the common number) = 1/6

$\begin{gathered} Pr(even\text{ number or less number than 4\rparen = Pr\lparen even number\rparen + Pr\lparen less than 4\rparen - Pr\lparen common number\rparen} \\ \\ Pr(even\text{ number or less number than 4\rparen= }\frac{3}{6}\text{ + }\frac{3}{6}-\frac{1}{6} \\ \\ Pr(even\text{ number or less number than 4\rparen= }\frac{3+3-1}{6} \\ \\ Pr(even\text{ number or less number than 4\rparen= 5/6} \end{gathered}$