Q6. - 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 (value at most $1)

Step-by-Step Solution

Answer

The probability of choosing a value at most $1 is 1.

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 value less than $1.”

 

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

 

The value of a nickel is $0.05.

 

The value of a dime is $0.10.

 

The value of a quarter is $0.25.

 

Finally, the value of a one-dollar coin is obviously $1.

 

So, the event “choosing a value at most $1” is equivalent to the event “choosing a nickel or dime or quarter or one-dollar coin”.

 

Since the jar contains 70 nickels, 100 dimes, 80 quarters, and 50 one-dollar coins,

$$\begin{gathered} n=70+100+80+50 \\ =300 \end{gathered}$$ 

So, $n=300$.

 

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

 

Then, $T=300$.

Step 4. Calculate the probability.

Put E : value at most $1, $n=300$ and $T=300$ in $P\left(E\right)=\frac{n}{T}$ to get,

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

So, $P\left(\mathrm{value} \mathrm{at} \mathrm{most} \$1\right)=1$

 

The probability of choosing a value less than $1 is 1.