A box contains a mixture of red, blue, and green tokens. There are exactly 16 red tokens i… — Armed Services Vocational Aptitude Battery (ASVAB)

A box contains a mixture of red, blue, and green tokens. There are exactly $16$ red tokens in the box. The probability of randomly selecting a red token is $\frac{2}{5}$ . If there are $14$ blue tokens in the box, what is the probability of randomly selecting a green token on a single draw?

$\frac{1}{4}$ Answer
B
$\frac{3}{5}$
C
$\frac{7}{20}$
D
$\frac{1}{3}$

Answer

The probability of randomly selecting a green token is

\frac{1}{4}

To find the probability of drawing a green token, you must first know the total number of tokens. Because the

16

red tokens make up

\frac{2}{5}

of the total, the total number of tokens is

16 \div \frac{2}{5} = 40

. The box contains

16

red and

14

blue tokens, accounting for

30

tokens. This leaves

10

green tokens (

40 - 30

). The probability of selecting a green token is the number of green tokens divided by the total number of tokens:

\frac{10}{40}

, which reduces to

\frac{1}{4}

Step-by-Step Solution

Determine the total number of tokens in the box.

Total tokens =

40

Since

16

red tokens represent a probability of

\frac{2}{5}

, we can find the total by dividing the part by its fraction:

16 \div \frac{2}{5} = 16 \times \frac{5}{2} = 40

Calculate the number of green tokens.

Green tokens =

10

Subtract the known red and blue tokens from the total:

40 - 16 \text{ (red)} - 14 \text{ (blue)} = 10 \text{ green tokens}

Calculate the probability of drawing a green token.

Probability =

\frac{1}{4}

Probability is the number of favorable outcomes divided by total outcomes:

\frac{10}{40}

, which simplifies to

\frac{1}{4}

Key Concept

Single Event Probability and Total Outcomes

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic