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 (dime)

Short answer

The probability of choosing a dime is $\frac{1}{3}$.

Step-by-step solution

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 dime.”

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

Since the jar contains 100 dimes, $n=100$.

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

Step 4. Calculate the probability.

Put $E:\mathrm{dime}$, $n=100$and $T=300$in $P\left(E\right)=\frac{n}{T}$to get,

$$\begin{gathered} P\left(\mathrm{dime}\right)=\frac{100}{300} \\ =\frac{1}{3} \end{gathered}$$

So,$P\left(\mathrm{dime}\right)=\frac{1}{3}$

The probability of choosing a dime is $\frac{1}{3}$.