Question

A very large bag contains more coins than you are willing to count. Instead, you draw a random sample of coins from the bag and record the following numbers of eachtype of coin in the sample before returning the sampled coins to the bag. If you randomly draw a single coin out of the bag, what is the probability that you will obtaineither a nickel or a penny? Enter a fraction or round your answer to 4 decimal places, if necessary.Quarters24Coins in a BagDimes Nickels2822Pennies26

Answer 1

First, find the probability for drawing a nickel and drawing a penny.

$\begin{gathered} P(N)=\frac{\text{number of sampled nickel}}{\text{total number of sampled coins}} \\ P(N)=\frac{22}{24+28+22+26} \\ P(N)=\frac{22}{100} \\ \\ P(Pn)=\frac{\text{number of sampled penny}}{\text{total number of sampled co}\imaginaryI\text{ns}} \\ P(Pn)=\frac{26}{22+28+22+26} \\ P(Pn)=\frac{26}{100} \end{gathered}$

Since finding a nickel and finding a penny are mutually exclusive events, then we can say that

$\begin{gathered} P(N\text{ or }Pn)=P(N\cup Pn) \\ P(N\cup Pn)=P(N)+P(Pn) \\ P(N\cup Pn)=\frac{22}{100}+\frac{26}{100} \\ P(N\cup Pn)=\frac{48}{100} \\ P(N\cup Pn)=0.48 \end{gathered}$

Therefore, the probability of finding a nickel or a penny is 0.48.