Question

chapter 1 section 2 example 1 your turn page 20 the tree diagram shows three out of nine possible outcomes result in the hat and glove same colour, p(m). p(m)=\frac{n(m)}{n(s)} =\frac{3}{9}=\frac{1}{3}

Explanation:

Step1: Identify total and favorable outcomes

There are 9 total outcomes in the sample - space $n(S)=9$, and 3 favorable outcomes for the event $M$ (hat and gloves of same color), so $n(M) = 3$.

Step2: Apply probability formula

The probability formula is $P(M)=\frac{n(M)}{n(S)}$. Substituting $n(M) = 3$ and $n(S)=9$ gives $P(M)=\frac{3}{9}$.

Step3: Simplify the fraction

Simplify $\frac{3}{9}$ to $\frac{1}{3}$.

Answer:

$\frac{1}{3}$