Question 1125217
A bag contains three 20-dollar bills, three 10-dollar bills, and three 5-dollar bills. Three bills are selected from the bag at random. Let the random variable X represent the total dollar value of the selected bills. 



What is the least possible value of X?<br> 
 
This happens when all three selections are each $5 bills, 3x5 = 15:
Ans:  {{{ highlight( 15 ) }}}  dollars<br>



What is the greatest possible value of X? 
This happens when all three selections are $20 bills:  3x20 = 60:
Ans:  {{{ highlight( 60 ) }}}  dollars<br> 



What is Pr(X=30)? 
Let F=five, T=ten, W=twenty selected  

Lets list the probabilities where a ten is selected first, then any of {F,T,W} for the remaining two:
Pr(TTT) = (3/9)(2/8)(1/7) = 6/504  
Pr(TTF) = (3/9)(2/8)(3/7) = 18/504 
Pr(TTW) = (3/9)(2/8)(3/7) = 18/504 
Pr(TWW) = 18/504
Pr(TFF) = 18/504
Pr(TWF) = 27/504
Pr(TFW) = 27/504
Pr(TFT) =  18/504
Pr(TWT) = 18/504<br>

Similarly for Pr(F,*,*) and Pr(W,*,*)      (not shown, but they follow the same pattern, for instance if you want Pr(F,W,F) just look above for Pr(T,W,T), mentally substituting "F" for "T" and you can see it is  18/504) <br>

Pr(X=30) = Pr(three tens)  +  Pr(two fives and one twenty)
Pr(X=30) = Pr(T,T,T) + Pr(F,F,W) + Pr(F,W,F) + Pr(W,F,F)
                =   6/504 +   18/504 + 18/504 + 18/504
                =  60/504
                =  {{{ highlight( 5/42 ) }}}   (about 0.1190 or 11.9%)