A box contains 4 quaters, 3 dimes, and 2 nickels. you draw out two coins and keep them both. What is the probability that both are quaters?
To find the probability of drawing two quarters from the box, we first need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
There are a total of 9 coins in the box (4 quarters + 3 dimes + 2 nickels). When you draw out two coins and keep them both, the first draw has 9 possibilities since any of the 9 coins can be selected. Then, for the second draw, there are only 8 coins left in the box. Thus, the total number of possible outcomes is 9 * 8 = 72.
Number of favorable outcomes:
Since we want to draw two quarters, we already know that the first draw must be a quarter, which leaves 3 remaining quarters in the box. For the second draw, there are 8 coins left in the box, including the remaining 3 quarters. So, the number of favorable outcomes is 4 * 3 = 12.
Probability:
The probability of an event happening is defined as the number of favorable outcomes divided by the total number of possible outcomes. In this case, the probability of drawing two quarters is 12/72, which simplifies to 1/6.
Therefore, the probability that both coins drawn are quarters is 1/6.