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You're at a clothing store that dyes your clothes while you wait. You get to pick from 4 pieces of clothing (shirt, pants, socks, or hat) and 3 colors (purple, blue, or orange). If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with socks that aren't blue?

You're at a clothing store that dyes your clothes while you wait. You get to pick from 44 pieces of clothing (shirt, pants, socks, or hat) and 33 colors (purple, blue, or orange).\newlineIf you randomly pick the piece of clothing and the color, what is the probability that you'll end up with socks that aren't blue?

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Full solution

Q. You're at a clothing store that dyes your clothes while you wait. You get to pick from 44 pieces of clothing (shirt, pants, socks, or hat) and 33 colors (purple, blue, or orange).\newlineIf you randomly pick the piece of clothing and the color, what is the probability that you'll end up with socks that aren't blue?
  1. Calculate Total Outcomes: Count total possible outcomes for picking any piece of clothing in any color.\newlineTotal outcomes = Number of clothing pieces ×\times Number of colors\newline=4×3= 4 \times 3\newline=12= 12
  2. Count Favorable Outcomes: Count the favorable outcomes for picking socks that aren't blue.\newlineFavorable outcomes = Number of colors (not blue) ×1\times 1 (for socks)\newline=2×1= 2 \times 1\newline=2= 2
  3. Calculate Probability: Calculate the probability of the favorable outcome. \newlineP(non-blue socks)=Favorable outcomesTotal outcomesP(\text{non-blue socks}) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}}\newline=212= \frac{2}{12}\newline=16= \frac{1}{6}

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