A box contains 3 green marbles and 2 blue marbles. 2 marbles are chosen without replacement. If both are blue, you win $10. If just one is blue you lose $3. Otherwise you lose $1. What is your expected gain or loss?

Question

campbell_st · Answer

2/7*1/6 *10 + 1/7*5/6*-3 + 5/7*4/6*-1

anonymous · Answer

how did you get that?

campbell_st · Answer

probability of selection 1 blue of 1st pick   2/7   blue on 2nd pick. 1/6

so its 2/7*1/6*10

next its 1st pick              probability blue = 2/7 
             2nd pick            not blue = 5/6

oops forgot 

probability not blue 1st pick 5/7 
probability blue 2nd pick 2/6 


and  1st pick  P not blue  5/7
         2nd pick   not blue = 4/6

the the expextation is the probability times financial return

2/7*1/6 *10 + 2/7*5*6*-3 +  5/7*2/6*-3 + 5/7*4/6*1

anonymous · Answer

how do you get the 7 for your denominator? There are only 5 marbles.

campbell_st · Answer

there are 7 marbles... in the box

campbell_st · Answer

if a selection is made and not put back in the box... there is only 6 to select from

anonymous · Answer

thanks!