Question

g.pr.10.2 (mc)

jenny needs to decide which nail polish and shoes to wear out to dinner. she lays out 5 bottles of nail polish of different colors: 2 shades of red and 3 shades of pink. she also lays out 4 pairs of different shoes: 3 are flats and 1 are high heels. if she chooses nail polish and shoes at random, find the probability she chooses a red nail polish and a pair of high heels.

\\(\bigcirc \frac{1}{20}\\)
\\(\bigcirc \frac{13}{20}\\)
\\(\bigcirc \frac{1}{3}\\)
\\(\bigcirc \frac{1}{10}\\)

Explanation:

Calculate the probability of choosing red nail polish

$$ P(\text{Red}) = \frac{2}{5} $$

Calculate the probability of choosing high heels

$$ P(\text{High Heels}) = \frac{1}{4} $$

Calculate the compound probability of both independent events

$$ P(\text{Red and High Heels}) = P(\text{Red}) \times P(\text{High Heels}) = \frac{2}{5} \times \frac{1}{4} = \frac{2}{20} = \frac{1}{10} $$

Answer:

• (A) \(\frac{1}{20}\)
• (B) \(\frac{13}{20}\)
• (C) \(\frac{1}{3}\)
• (D) \(\frac{1}{10}\) (Correct answer)