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$A box is filled with 2 yellow cards, 2 red cards, and 12 brown cards. A card is chosen at random from the box. What is the probability that the card is not red? Write your answer as a fraction in simplest form.$

A box is filled with $2$ yellow cards, $2$ red cards, and $12$ brown cards. A card is chosen at random from the box. What is the probability that the card is not red? $\newline$ Write your answer as a fraction in simplest form.

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Theoretical probability

Full solution

Q. A box is filled with

2

yellow cards,

2

red cards, and

12

brown cards. A card is chosen at random from the box. What is the probability that the card is not red?

\newline

Write your answer as a fraction in simplest form.

Count Total Cards: Count the total number of cards in the box. There are $2$ yellow, $2$ red, and $12$ brown cards. Total = $2 + 2 + 12 = 16$ cards.
Identify Non-Red: Identify the number of non-red cards. Since there are $2$ red cards, the rest are non-red. Non-red cards $=$ Total cards $-$ Red cards $= 16 - 2 = 14$ cards.
Calculate Probability: Calculate the probability of drawing a non-red card. Probability = Number of non-red cards / Total number of cards = $\frac{14}{16}$ .
Simplify Fraction: Simplify the fraction for the probability. $\frac{14}{16}$ simplifies to $\frac{7}{8}$ .

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