Question

An urn contains six 2 dollar coins, four 5 dollar coins, and three 1 dollar coins. Three coins are chosen randomly what is the probability that the three coins chosen are 5 dollar coins.A)5/286B)1/286C)3/286D) 4/286

Answer 1

Answer:

D) 4/286

Step-by-step explanation:

Let's organize the data in a table:

Number of coins Value of Coin

6 2$

4 5$

3 1$

Total: 13 coins

The probability one randomly selected coin is a 5$ dolar coin is:

$\begin{gathered} P_1=\frac{number\text{ of 5\ coin}}{\text{total of coins}} \\ P_1=\frac{4}{13} \end{gathered}$

After this, there will be 12 remaining coins (and three 5$ coins).

So, the probability that the second coin is a $5 coin:

$P_2=\frac{3}{12}$

After this, there will be 11 remaining coins (and two 5$ coins).

So, the probability that the third coin is a $5 coin:

$P_3=\frac{2}{11}$

So, the probability that the three coins are 5$ coins is the product of the three coins.

$\begin{gathered} P=P_1\cdot P_2\cdot P_3 \\ P=\frac{4}{13}\cdot\frac{3}{12}\cdot\frac{2}{11} \\ P=\frac{24}{1716}=\frac{4}{286} \end{gathered}$