Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following:
8
Pennies 22
Dimes
15
Nickels 12
Quarters
What is the probability that you reach into the jar and randomly grab a nickel and then, without replacement, a quarter? Express your answer as a fraction or a decimal number rounded to four decimal places.
To find the probability of randomly grabbing a nickel and then a quarter, we first need to determine the total number of coins in the jar.
Total number of coins = 8 (pennies) + 22 (dimes) + 15 (nickels) + 12 (quarters) = 57 coins
So, the probability of randomly grabbing a nickel first is: P(nickel) = Number of nickels / Total number of coins = 15 / 57
After grabbing a nickel, the total number of coins reduces to 56, of which there are 12 quarters left.
So, the probability of randomly grabbing a quarter after grabbing a nickel is: P(quarter | nickel) = Number of quarters left / Total number of coins after grabbing a nickel = 12 / 56
Therefore, the probability of randomly grabbing a nickel and then a quarter is: P(nickel and quarter) = P(nickel) * P(quarter | nickel) = (15/57) * (12/56) ≈ 0.0373
So, the probability is approximately 0.0373 when rounded to four decimal places.