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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

Initial Probability Calculation: Current probability of drawing a peppermint candy is $\frac{1}{5}$ , which means there are $5$ peppermint candies in the jar of $25$ candies.
Setting up Equation: We want the probability to be $\frac{1}{3}$ . Let $x$ be the number of peppermint candies to add.
Cross Multiplication: The new total number of candies will be $25 + x$ .
Solving for x: The new probability will be $(5 + x) / (25 + x) = \frac{1}{3}$ .
Final Result: Cross multiply to solve for $x$ : $3(5 + x) = 1(25 + x)$ .
Final Result: Cross multiply to solve for $x$ : $3(5 + x) = 1(25 + x)$ . $15 + 3x = 25 + x$ .
Final Result: Cross multiply to solve for $x$ : $3(5 + x) = 1(25 + x)$ . $15 + 3x = 25 + x$ .Subtract $x$ from both sides: $2x = 10$ .
Final Result: Cross multiply to solve for $x$ : $3(5 + x) = 1(25 + x)$ . $15 + 3x = 25 + x$ .Subtract $x$ from both sides: $2x = 10$ .Divide both sides by $2$ : $x = 5$ .

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