Q3. - 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 or nickel)

Step-by-Step Solution

Answer

The probability of choosing a quarter or nickel is $\frac{1}{2}$.

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(E) denotes the probability of the event E, n denotes the number of favorable outcomes and T 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 or nickel.”

 

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

 

Since the jar contains 80 quarters and 70 nickels,

$$\begin{gathered} n=80+70 \\ =150 \end{gathered}$$

So, $n=150$.

 

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

 

Then, $T=300$.

Step 4. Calculate the probability.

Put $E:\mathrm{quarter} \mathrm{or} \mathrm{nickel}$, $n=150$ and $T=300$ in $P\left(E\right)=\frac{n}{T}$ to get,

$\begin{array}{c}P\left(\mathrm{quarter} \mathrm{or} \mathrm{nickel}\right)=\frac{150}{300}\\ =\frac{1}{2}\end{array}$

So, $P\left(\mathrm{quarter} \mathrm{or} \mathrm{nickel}\right)=\frac{1}{2}$

 

The probability of choosing a quarter or nickel is $\frac{1}{2}$.