Q1. - Algebra 1

Question

One coin is randomly selected from a jar containing 70 nickels, 100 dimes, 80 quarters, and 50 one-dollar coins. Find each probability.

P (quarter)

Step-by-Step Solution

Answer

The probability of choosing a quarter is $\frac{4}{15}$.

Step 1. State the formula.

The formula for the probability of an event is $P\left(E\right)=\frac{n}{T}$, where E denotes the event, $P\left(E\right)$ denotes the probability of the event E, n denotes the number of favorable outcomes, and denotes the total number of outcomes.

Step 2. List the given data.

The jar contains 70 nickels, 100 dimes, 80 quarters and 50 one-dollar coins.

Step 3. Explanation.

The event is “choosing a quarter.”

 

The jar contains 70 nickels, 100 dimes, 80 quarters, and 50 one-dollar coins.

Since the jar contains 80 quarters, $n=80$.

The total number of coins in the jar is $70+100+80+50=300$. Then, $T=300$.

Step 4. Calculate the probability.

Put $E:\mathrm{quarter}$, $n=80$ and $T=300$ in $P\left(E\right)=\frac{n}{T}$ to get,

$$\begin{gathered} P\left(\mathrm{quarter}\right)=\frac{80}{300} \\ =\frac{8}{30} \\ =\frac{4}{15} \end{gathered}$$

So, $P\left(\mathrm{quarter}\right)=\frac{4}{15}$.

The probability of choosing a quarter is $\frac{4}{15}$.