Respuesta :
Answer:
The expected value of betting $500 on red is $463.7.
Step-by-step explanation:
There is not a fair game. This can be demostrated by the expected value of betting a sum of money on red, for example.
The expected value is calculated as:
[tex]E(G)=\sum p_iG_i[/tex]
being G the profit of each possible result.
If we bet $500, the possible outcomes are:
- Winning. We get G_w=$1,000. This happens when the roulette's ball falls in a red place. The probability of this can be calculated dividing the red slots (half of 36) by the total slots (38) of the roulette:
[tex]P(R)=R/T=18/38\approx0.4737[/tex]
- Losing. We get G_l=$0. This happens when the ball does not fall in a red place. The probability of this is the complementary of winning, so we have:
[tex]P(not \,R)=1-P(R)=1-18/38=20/38\approx 0.5263[/tex]
Then, we can calculate the expected value as:
[tex]E(G)=\sum p_iG_i=p_wG_w+p_lG_l=0.4637*1,000+0.5263*0=463.7[/tex]
We expect to win $463.7 for every $500 we bet on red, so we are losing in average $36.3 per $500 bet.
