Question

A cash register contains 5 $10 bills and 3 $5 bills. you randomly pick 4 bills.

a. what is the probability you pick exactly two $10 bills?
b. what is the probability you pick at most one $5 bill?

Answer 1

a. The probability of picking exactly two $10 bills is
`(3)/(7)`

b. The probability of picking at most one $5 bill is
`(1)/(2)`

Step-by-step explanation

Number of $10 bills
`= 5`

and number of $5 bills
`= 3`

Total number of bills= 5+3 = 8. You need to randomly pick 4 bills, so the total possible outcome
`= ^8C^4`

a.

For getting exactly two $10 bills, you need to pick two $10 bills and two $5 bills. That means we will pick two $10 bill from 5 bills and two $5 bills from 3 bills.

So, the probability
`=((^5C^2)*(^3C^2))/(^8C^4) =(10*3)/(70)=(30)/(70)=(3)/(7)`

b.

For getting at most one $5 bill, you need to pick either zero or one $5 bill.

If you pick zero $5 bill, that means there are four $10 bills

and if you pick one $5 bill, that means there are three $10 bills.

So, the probability
`=((^3C^0*^5C^4)+(^3C^1*^5C^3))/(^8C^4)=((1*5)+(3*10))/(70)=(5+30)/(70)=(35)/(70)=(1)/(2)`