Question

this tree diagram represents the possible outcomes.
what is the probability that sebastian spins a c and then spins an even number?
options: \\(\frac{1}{15}\\), \\(\frac{2}{15}\\), \\(\frac{1}{5}\\), \\(\frac{2}{5}\\)

Explanation:

Step1: Find probability of spinning C

There are 3 options (A, B, C), so \( P(C)=\frac{1}{3} \).

Step2: Find probability of even number after C

Numbers: 1,2,3,4,5. Even numbers: 2,4 (2 numbers). So \( P(\text{even} | C)=\frac{2}{5} \).

Step3: Multiply the two probabilities

\( P(C \text{ and even}) = P(C) \times P(\text{even} | C) = \frac{1}{3} \times \frac{2}{5} = \frac{2}{15} \).

Answer:

\(\frac{2}{15}\) (corresponding to the option \(\frac{2}{15}\))