Question

a single die is rolled one time. find the probability of rolling a number greater than 5 or less than 4. the probability is (simplify your answer.)

Explanation:

Step1: Determine the sample space

A die has 6 faces, so the sample space \(n(S)=6\).

Step2: Find the number of favorable outcomes

Numbers greater than 5: \(6\) (1 number).
Numbers less than 4: \(1,2,3\) (3 numbers).
Using the formula for \(P(A\cup B)=P(A)+P(B)\) (since \(A\) and \(B\) are mutually - exclusive events, \(A\cap B = \varnothing\)).
\(n(A) = 1\), \(n(B)=3\), so \(n(A\cup B)=1 + 3=4\).

Step3: Calculate the probability

The probability formula is \(P=\frac{n(A\cup B)}{n(S)}\).
Substitute \(n(A\cup B) = 4\) and \(n(S)=6\) into the formula: \(P=\frac{4}{6}=\frac{2}{3}\).

Answer:

\(\frac{2}{3}\)