If  is a random variable representing your winnings from playing the game, then it has support
 is a random variable representing your winnings from playing the game, then it has support

There are 52 cards in the deck. Only the 1s, 2s, and 3s fulfill the first condition, so there are 12 ways in which you can win $43. So  has PMF
 has PMF

You can expect to win
![E[W]=\displaystyle\sum_ww\,P(W=w)=\frac{43\cdot3}{13}-\frac{11\cdot10}{13}=\boxed{\frac{19}{13}}](https://tex.z-dn.net/?f=E%5BW%5D%3D%5Cdisplaystyle%5Csum_ww%5C%2CP%28W%3Dw%29%3D%5Cfrac%7B43%5Ccdot3%7D%7B13%7D-%5Cfrac%7B11%5Ccdot10%7D%7B13%7D%3D%5Cboxed%7B%5Cfrac%7B19%7D%7B13%7D%7D)
or about $1.46 per game.
 
        
             
        
        
        
14/21 is 2/3 simplified.
9/15 is 3/5 simplified.
and 3/8 can not be simplified, so it's 3/8
        
                    
             
        
        
        
Answer:
Step-by-step explanation:
0.1322 ≅ 0.13
 
        
                    
             
        
        
        
The rate for one unit of a given quantity is called a(n) Unit Rate.