I can't figure out how to do a probability problem?

Question

Five raffle tickets are sold for a Halloween raffle. Marty buys three of the five raffle tickets. Two of the tickets are to be drawn as winning tickets. What is the probability of Marty not having a winning ticket? What is the probability of Marty have one winning ticket? What is the probability of Marty having two winning tickets?

 

Please help me start. 

Answer 1

Now, you have to know the total number of ways to draw 3 of the five tickets so you do the combination: 5 nCr 3

Let W represent winning

Let L represent losing

 

Question 1

What is the probability of Marty not having a winning ticket?

 

What it means is that in all 3 draws of the tickets, none of them are the winning ticket so,

 

                     (L = 3)  (W = 0)                              

(total number of ways to draw 3 of the five tickets)

 

= (3 nCr 3)(2 nCr 0)  = (1)(1)  =  1   = 0.1

          (5 nCr 3)              10        10

 

 

Question 2

What is the probability of Marty having one winning ticket?

                  (L = 2)  (W = 1)                                 
(total number of ways to draw 3 of the five tickets)

= (3 nCr 2)(2 nCr 1) = (3)(2) =  6  = 0.6
          (5 nCr 3)             10       10

 

 

Question 3

What is the probability of Marty having two winning tickets?

 

                  (L = 1)  (W = 2)                                 
(total number of ways to draw 3 of the five tickets)

= (3 nCr 1)(2 nCr 2) = (3)(1) = 3  = 0.3
         (5 nCr 3)              10      10