Question

bob has a coin cup with four $1 tokens and two $5 tokens in it. he also has two $10 tokens and one $25 token in his pocket. he randomly draws a token from the cup, and then randomly draws a token from his pocket. what is the probability that he will draw $30 in tokens?
a. $\frac{1}{9}$
b. $\frac{4}{9}$
c. $\frac{1}{3}$
d. $\frac{2}{9}$

Explanation:

Step1: Calculate total tokens in cup

There are \(4 + 2=6\) tokens in the cup.

Step2: Calculate total tokens in pocket

There are \(2 + 1 = 3\) tokens in the pocket.

Step3: Find combinations that sum to $30

The combinations that sum to $30 are: ($5 from cup and $25 from pocket) or ($1 from cup and $29 is not possible, so only the first - mentioned combination).
The probability of drawing a $5 token from the cup is \(\frac{2}{6}=\frac{1}{3}\).
The probability of drawing a $25 token from the pocket is \(\frac{1}{3}\).

Step4: Use multiplication rule for independent events

Since the draws are independent events, the probability of both events occurring is the product of their individual probabilities. So \(P=\frac{1}{3}\times\frac{1}{3}=\frac{1}{9}\).

Answer:

A. \(\frac{1}{9}\)