Question

Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following = 5 pennies, 28 dimes, 17 nickels, 6 quartersWhat is the probability that you reach into the jar and randomly grab a dime and then, without replacement, a quarter? Express your answer as a fraction or a decimal rounded four decimal places

Answer 1

We have to calculate the probability of drawing a dime and then a quarter, without replacement.

We will calculate the probability as the product of the probabilities of two events.

The probability of drawing a dime in the first draw is equal to the quotient between the number of dimes and the number of coins:

$P(D)=\frac{D}{P+D+N+Q}=\frac{28}{5+28+17+6}=\frac{28}{56}=0.5$

Now, we have to calculate the probability of drawing a quarter.

As the dime that was drawn in the first draw is not replaced, we have one coin less.

Then, we can calculate the probability of drawing a quarter as:

$P(Q)=\frac{6}{55}\approx0.10909$

We can now calculate the probability of this two events happening as:

$\begin{gathered} P=P(D)\cdot P(Q) \\ P=\frac{1}{2}*\frac{6}{55}=\frac{3}{55}\approx0.0545 \end{gathered}$

Answer: The probability is 0.0545.