Question

1. johnny has three shirts (blue, red, yellow) three pairs of pants (blue, black, brown) and two hats (white, black) to choose from to wear to school. complete the tree diagram. write all answers as a fraction, decimal and percent

hat
white
black
shirt
pants
i) total number of outcomes: ______
ii) p (white hat, red shirt and blue pants) =
iii) p (black hat, and brown pants)

Explanation:

i) Total number of outcomes

Step1: Identify number of choices

Hats: 2 (White, Black), Shirts: 3 (blue, red, yellow), Pants: 3 (blue, black, brown).

Step2: Use multiplication principle

Total outcomes = Hats × Shirts × Pants = \( 2 \times 3 \times 3 \)

Step3: Calculate the product

\( 2 \times 3 \times 3 = 18 \)

Step1: Determine favorable and total

Favorable: 1 (White hat, Red shirt, blue pants). Total: 18 (from part i).

Step2: Find probability as fraction

Probability = \( \frac{1}{18} \)

Step3: Convert to decimal

\( \frac{1}{18} \approx 0.0556 \)

Step4: Convert to percent

\( \frac{1}{18} \times 100 \approx 5.56\% \)

Step1: Determine favorable outcomes

Black hat: 1 choice. Brown pants: 1 choice. Shirts: 3 choices (since any shirt is allowed). So favorable = \( 1 \times 3 \times 1 = 3 \). Total: 18.

Step2: Find probability as fraction

Probability = \( \frac{3}{18} = \frac{1}{6} \)

Step3: Convert to decimal

\( \frac{1}{6} \approx 0.1667 \)

Step4: Convert to percent

\( \frac{1}{6} \times 100 \approx 16.67\% \)

Answer:

18

ii) \( P(\text{White hat, Red shirt and blue pants}) \)