Question

the spinner is equally likely to land on any of the five sections. what is the probability that the spinner lands on an even number or on the unshaded section? 1/5 2/5 3/5 4/5

Explanation:

Step1: Determine the total number of sections

The spinner has 5 sections. So the total number of possible outcomes \( n(S)=5 \).

Step2: Identify the favorable outcomes

The even - numbered sections are 2 and 4. The un - shaded section is 3. But we need to use the formula for the probability of \( A\cup B\): \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the event of landing on an even number (\(A = \{2,4\}\)) and \(B\) be the event of landing on the un - shaded section (\(B=\{3\}\)). Since \(A\cap B=\varnothing\) (no common elements), \(P(A)=\frac{2}{5}\) (because \(n(A) = 2\)), \(P(B)=\frac{1}{5}\) (because \(n(B)=1\)).

Step3: Calculate the probability

Using the formula \(P(A\cup B)=P(A)+P(B)\), we substitute the values: \(P(A\cup B)=\frac{2 + 1}{5}=\frac{3}{5}\).

Answer:

\(\frac{3}{5}\) (the third option)