Please help to solve this probability question

Quote:

Originally Posted by mathconfuser

Hi, I am new to this forum and would like to ask for your help on the below question:

Fred and Jose are experimenting with a new game. The probability Fred wins a round of this game is 1/3 and for Jose the probability to wins a round is 2/3. They decide that to make the game fair, Fred scores 3 pts when he wins a round, and Jose scores 2 pts when wins a round.

B) How many pts per round can each player expect to win? That is, what is the expected value for each player??

I would like to thank all and especially the admins of this forum because it is so helpful for my confusing math solving ability.

i believe the expected value is just the sum off all outcomes for each player, multiplied by the payoff of those outcomes.

i assume a player is not penalized for losing. so if a player loses, he simply gets zero points.

expected value for Fred:

E(F) = (Probabilty of win)(payoff for winning) + (Probability of losing)(payoff for losing)
.......= (1/3)(3) + (2/3)(0)
.......= 1

so Fred can expect to gain 1 point per round.

expected value for Jose:

E(J) = (Probabilty of win)(payoff for winning) + (Probability of losing)(payoff for losing)
.......= (2/3)(2) + (1/3)(0)
.......= 4/3

so Jose can expect to gain 4/3 points per round.

Disclaimer: I am not good with probability, I haven't done it in ages, so you should wait until someone verifies this if you can