SOLUTION: Dad puts $5 bill and three $1 bills in he first box.In a second box, he puts another $5 bill with just $1 bill. For washing the car, Junior gets to take out a bill from the first b

Algebra ->  Probability-and-statistics -> SOLUTION: Dad puts $5 bill and three $1 bills in he first box.In a second box, he puts another $5 bill with just $1 bill. For washing the car, Junior gets to take out a bill from the first b      Log On


   

Question 625356: Dad puts $5 bill and three $1 bills in he first box.In a second box, he puts another $5 bill with just $1 bill. For washing the car, Junior gets to take out a bill from the first box without looking and put it in the second box. After these are well mixed, he then gets to take one bill from the second box. What is the probability that he will get $5?
Answer by Edwin McCravy(20059) About Me  (Show Source):
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Dad puts $5 bill and three $1 bills in he first box.In a second box, he puts another $5 bill with just $1 bill. For washing the car, Junior gets to take out a bill from the first box without looking and put it in the second box. After these are well mixed, he then gets to take one bill from the second box. What is the probability that he will get $5?

We begin with:

First box         Second box
$5+$1+$1+1$         $5+$1

Junior gets to take out a bill from the first box without looking and put it in the second box.

Then we have either of these cases:

Case 1, with a probability of 1/4

First box         Second box
$1+$1+1$           $5+$5+$1

and

Case 2, with a probability of 3/4

First box         Second box
$5+$1+$1           $5+$1+$1

he then gets to take one bill from the second box

So,

P($5) = P[(case 1 AND drawing a 5$) OR (case 2 AND drawing a $5)]

= P(case 1)×P(drawing a $5 given case 1) + P(case 2)×P(drawing a $5 given case 2) =

(1/4)(2/3) + (3/4)(1/3) = 5/12

Edwin