more probability I can't understand

Question

a large bucket contains 150 lottery tickets. one ticket is worth $100, four tickets are worth $50, six tickets are worth $25, fifteen tickets win $10, and the rest are worthless. two tickets are chosen at random. suppose that the net winning is equal to the worth of the ticket that gives the smaller amount won. find the expected value of net winning. 

Answer 1

 

Hi Jay,

 

For the case by which we can win $50,

we need to choose "a $100 ticket followed by a $50 one",

"a $50 ticket followed by a $100 one", or

"a $50 ticket followed by a $50 one".

So, the probability we can win $50 is

     (1/150)·(4/149) + (4/150)·(1/149) + (4/150)·(3/149)

        = 20/(150·149)

        = 20/22,350

 

Following the same logic as above,

we can derive the following probabilities.

The probability we can win $25 = 90/22,350

The probability we can win $10 = 540/22,350

The probability we can win $0 = 21,700/22,350

 

So, the expected value of winning is

     50·(20/22,350) + 25·(90/22,350) + 10·(540/22,350)

         = 8,650/22,350

         = 0.39

 

It's 39 cents.