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, we need to determine the total number of coins in the jar:
Total coins = 5 pennies + 28 dimes + 17 nickels + 29 quarters
Total coins = 79 coins
Next, we need to calculate the probability of drawing a quarter first:
Probability of drawing a quarter = Number of quarters / Total coins
Probability of drawing a quarter = 29 / 79
Now, we need to calculate the probability of drawing a nickel after having already drawn a quarter:
Probability of drawing a nickel = Number of nickels / (Total coins - 1)
Probability of drawing a nickel = 17 / 78
Therefore, the probability of first drawing a quarter and then a nickel without replacement is:
(29/79) * (17/78) ≈ 0.0924
So, the probability is approximately 0.0924 or 9.24%.