Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following:
17 Pennies 9 Dimes
19 Nickels 25 Quarters
What is the probability that you reach into the jar and randomly grab a quarter and then, without replacement, a dime? 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:
Total = 17 (pennies) + 9 (dimes) + 19 (nickels) + 25 (quarters) = 70
Now, let's calculate the probability of picking a quarter first:
P(quarter) = Number of quarters / Total number of coins = 25/70 = 5/14
After picking a quarter, there will be 69 coins left in the jar (since we didn't replace the quarter we took out). Now, let's calculate the probability of picking a dime next:
P(dime) = Number of dimes / Total number of coins remaining = 9/69
Finally, let's calculate the probability of picking a quarter first and then a dime:
P(quarter and dime) = P(quarter) * P(dime) = (5/14) * (9/69) ≈ 0.0918
Therefore, the probability of randomly grabbing a quarter and then, without replacement, a dime is approximately 0.0918 (rounded to four decimal places).