Find the probability model of your net gain.

Question

A Nevada roulette wheel had 38 pockets, labeled as 0 00 1 2 3 ... 35 36. One bet is single number. If you bet $1 on a number (any one between 1 and 36) and the number comes up, you get the dollar back together with $35 in winnings; otherwise, you lose your dollar.

A.) Find the probability model of your net gain.

B.) Find the mean of your net gain for one bet.

Answer 1

A.) The probability model of your net gain is 1/38 for a gain of $35 and 37/38 for a loss of -$1.

B.) The mean of your net gain for one bet is  (1/38)($35) + (37/38)(-$1) = -$ (2/38) = -$ (1/19).

Answer 2

There are only two outcomes for a bet:  a Win (W) or a loss (L).

The probability of a W is 1/38,  the probability of a L is   37/38.   The  average payout for a bet is therefore

 

(1/38) (35 +1)  + (37/38) 0  =   36/38 =  18/19 =  .9474    ($.95  for a $1 bet)

 

The gain is actually a loss of  $0.05    per $1 bet.

 

 

Answer 3

a)   P(w) = 1/38

 

b)  E(x) = np= n / 38   n is the number of bits.