Question

what is the probability of getting a 6 \or\ an odd number when rolling a single die?
a 1/6
b 1/3
c 1/2
d 2/3

Explanation:

Step1: Calculate total outcomes

A die has 6 faces. So total number of outcomes \(n(S)=6\).

Step2: Define events

Let \(A\) be the event of getting a 6. \(n(A) = 1\). Let \(B\) be the event of getting an odd number (\(1,3,5\)). \(n(B)=3\).

Step3: Check for mutual - exclusivity

Events \(A\) and \(B\) are mutually - exclusive (no common elements).

Step4: Use probability formula for mutually - exclusive events

\(P(A\cup B)=P(A)+P(B)\). \(P(A)=\frac{n(A)}{n(S)}=\frac{1}{6}\), \(P(B)=\frac{n(B)}{n(S)}=\frac{3}{6}\).

Step5: Calculate the probability

\(P(A\cup B)=\frac{1 + 3}{6}=\frac{4}{6}=\frac{2}{3}\).

Answer:

D. \(2/3\)