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 find the total number of coins in the jar:
Total number of coins = 5 (pennies) + 28 (dimes) + 17 (nickels) + 29 (quarters) = 79.
The probability of getting a quarter on the first draw is:
P(quarter) = Number of quarters / Total number of coins = 29 / 79 ≈ 0.3671.
After removing one quarter from the jar, the total number of coins becomes 78. The probability of getting a nickel on the second draw is:
P(nickel) = Number of nickels / Total number of coins = 17 / 78 ≈ 0.2179.
Therefore, the probability of randomly grabbing a quarter and then a nickel, without replacement, is:
P(quarter) * P(nickel) = 0.3671 * 0.2179 ≈ 0.0800.
So, the probability rounded to four decimal places is 0.0800.