suppose you have a wallet with $5 bills, $10 bills, and $20 bills. if the probability of picking 10 dollar bill is 4/15, and the probability of picking 5 dollar bill is 1/3, what is the probability of picking a 20 dollar bill?
a. 1/15
b. 1/5
c. 4/15
d. 2/5***
1-(4/15 + 1/3) = 6/15 = 2/5
good job
To find the probability of picking a $20 bill, we can use the information provided:
Probability of picking a $10 bill = 4/15
Probability of picking a $5 bill = 1/3
We are given the total number of denominations: $5, $10, and $20 bills.
Let's assign variables for the probabilities:
P($10 bill) = 4/15
P($5 bill) = 1/3
Let's assume the probability of picking a $20 bill is P($20 bill).
Since these are the only three denominations available in the wallet, the sum of the probabilities should equal 1.
Therefore, we have the equation:
P($10 bill) + P($5 bill) + P($20 bill) = 1
4/15 + 1/3 + P($20 bill) = 1
Multiplying both sides by the lowest common denominator of 15 to eliminate the fractions:
(4/15) * 15 + (1/3) * 15 + (P($20 bill)) * 15 = 1*15
4 + 5 + 15(P($20 bill)) = 15
15(P($20 bill)) = 15 - 9
15(P($20 bill)) = 6
Dividing both sides by 15:
P($20 bill) = 6/15
Simplifying the fraction:
P($20 bill) = 2/5
Therefore, the correct answer is d. 2/5
To find the probability of picking a $20 bill, we can subtract the probabilities of picking a $5 bill and a $10 bill from 1, since those are the only three options.
Let's calculate the probability of picking a $5 bill first. The probability of picking a $5 bill is given as 1/3.
Next, let's calculate the probability of picking a $10 bill. The probability of picking a $10 bill is given as 4/15.
To calculate the probability of picking a $20 bill, we can subtract the sum of the probabilities of picking a $5 bill and a $10 bill from 1.
So, the probability of picking a $20 bill is:
1 - (1/3 + 4/15) = 1 - (5/15 + 4/15) = 1 - 9/15 = 6/15 = 2/5.
Therefore, the correct answer is d. 2/5.