Question

You have four $20 bills, ten $5 bills, and twelve $1 bills in your wallet. If you reach into your wallet twice, what is the probability that you will pull out a $1 bill the first time and a $5 bill the second time?

Answer 1

The total number of banknotes you have in your wallet is:

4 $20 bills + 10 $5 bills + 12 $1 bills = 4 + 10 + 12 = 26 bills

For the first time, you have 12 $1 bills, so the probability of pulling out a $1 bill is:

Probability of pulling out a $1 bill the first time = (number of $1 bills) / (total number of bills) = 12 / 26 ≈ 0.4615

After pulling out a $1 bill, you now have 11 remaining $1 bills in your wallet.

For the second time, you have 10 $5 bills, so the probability of pulling out a $5 bill is:

Probability of pulling out a $5 bill the second time = (number of remaining $5 bills) / (total number of remaining bills) = 10 / 25 = 0.4

Now, to get the probability of rolling out a $1 bill the first time and a $5 bill the second time, we simply need to multiply the probabilities of the two independent events:

Overall probability = Probability of pulling out a $1 bill the first time * Probability of pulling out a $5 bill the second time

Overall probability ≈ 0.4615 * 0.4 ≈ 0.1846

The probability of getting a $1 bill the first time and a $5 bill the second time is about 0.1846, or about 18.46%.