Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following:
5 Pennies 28 Dimes
17 Nickels 29 Quarters
What is the probability that you reach into the jar and randomly grab a quarter and then, without replacement, a nickel? Express your answer as a fraction or a decimal number rounded to four decimal places.
First, let's calculate the total number of coins in the jar:
5 Pennies + 28 Dimes + 17 Nickels + 29 Quarters = 79 coins
The probability of grabbing a quarter on the first attempt is: 29 Quarters / 79 total coins = 29/79
After taking out one quarter, there are now 78 coins left in the jar. The probability of grabbing a nickel on the second attempt is: 17 Nickels / 78 remaining coins = 17/78
Therefore, the overall probability is: (29/79) * (17/78) = 493/5922 ≈ 0.0833
So, the probability of grabbing a quarter and then a nickel from the jar is approximately 0.0833.