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The probability of drawing a peppermint candy out of a jar of $25$ candies is $\frac{1}{5}$ . How many more peppermint candies should be added to the jar in order to increase the probability of drawing a peppermint candy to $\frac{1}{3}$ ? $\newline$ A. $2$ $\newline$ B. $5$ $\newline$ C. $10$ $\newline$ D. $30$

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Find probabilities using the addition rule

Full solution

Q. The probability of drawing a peppermint candy out of a jar of

25

candies is

\frac{1}{5}

. How many more peppermint candies should be added to the jar in order to increase the probability of drawing a peppermint candy to

\frac{1}{3}

?

\newline

A.

2

\newline

B.

5

\newline

C.

10

\newline

D.

30

Calculate peppermint candies: Current probability of drawing a peppermint candy is $\frac{1}{5}$ . There are $25$ candies in total, so there must be $25 \times \left(\frac{1}{5}\right) = 5$ peppermint candies.
Determine new probability: We want the probability to be $\frac{1}{3}$ . Let $x$ be the number of peppermint candies to add. The new total will be $25 + x$ candies.
Set up equation: The new probability will be $(5 + x) / (25 + x) = \frac{1}{3}$ .
Solve for x: Cross-multiply to solve for x: $3 \times (5 + x) = 1 \times (25 + x)$ .
Substitute $x$ : $15 + 3x = 25 + x$ .
Simplify equation: Subtract $x$ from both sides: $2x = 10$ .
Find final value: Divide both sides by $2$ : $x = 5$ .

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