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After growing tired of squinting while driving, Desmond went shopping for a pair of sunglasses. He tried on glasses with different frames and lenses.





Cat eye frames
Browline frames
Aviator frames


Polarized lenses
2
8
7


Regular lenses
7
4
8




What is the probability that a randomly selected pair of sunglasses has cat eye frames and does not have regular lenses?
Simplify any fractions.

After growing tired of squinting while driving, Desmond went shopping for a pair of sunglasses. He tried on glasses with different frames and lenses.\newline\begin{tabular}{|l|c|c|c|}\newline\cline { 22 - 44 } & Cat eye frames & Browline frames & Aviator frames \\\newline\hline Polarized lenses & 22 & 88 & 77 \\\newline\hline Regular lenses & 77 & 44 & 88 \\\newline\hline\newline\end{tabular}\newlineWhat is the probability that a randomly selected pair of sunglasses has cat eye frames and does not have regular lenses?\newlineSimplify any fractions.

Full solution

Q. After growing tired of squinting while driving, Desmond went shopping for a pair of sunglasses. He tried on glasses with different frames and lenses.\newline\begin{tabular}{|l|c|c|c|}\newline\cline { 22 - 44 } & Cat eye frames & Browline frames & Aviator frames \\\newline\hline Polarized lenses & 22 & 88 & 77 \\\newline\hline Regular lenses & 77 & 44 & 88 \\\newline\hline\newline\end{tabular}\newlineWhat is the probability that a randomly selected pair of sunglasses has cat eye frames and does not have regular lenses?\newlineSimplify any fractions.
  1. Calculate Total Sunglasses: Total sunglasses = sum of all glasses with different frames and lenses.\newlineTotal sunglasses = (2+8+7)+(7+4+8)=17+19=36(2 + 8 + 7) + (7 + 4 + 8) = 17 + 19 = 36.
  2. Identify Cat Eye Frames: Cat eye frames with polarized lenses =2= 2.
  3. Calculate Probability: Probability = Number of cat eye frames with polarized lensesTotal sunglasses\frac{\text{Number of cat eye frames with polarized lenses}}{\text{Total sunglasses}}.\newlineProbability = 236\frac{2}{36}.
  4. Simplify Fraction: Simplify the fraction 236\frac{2}{36}.\newlineProbability = 118\frac{1}{18}.

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