Two teams have played each other 14 times. Team A won 9 games and team B won 5 games. Bob offers to bet $6 on team A winning while you bet $4 on team B winning. The winner gets $10. How much money should you expect to lose on such a bet? (Round to the nearest cent.)
E(x) = (5/14)*6 - (9/14)*4 = -3/7 So you would expect to lose approx 43 cents
To calculate the expected loss, we need to calculate the probability of each outcome happening.
Out of the 14 games played, team A won 9 games. The probability of team A winning a game is 9/14.
Similarly, team B won 5 games out of 14, so the probability of team B winning is 5/14.
Let's calculate the expected loss:
Expected Loss = (Probability of Team A winning) × (Amount You Bet on Team B) + (Probability of Team B winning) × (Amount Bob Bets on Team A)
Expected Loss = (9/14) × $4 + (5/14) × $6
Expected Loss = $2.57
Therefore, you should expect to lose approximately $2.57 on such a bet.
To calculate the expected loss, we need to find the probability of each team winning and then determine the amount of money that would be lost in each scenario.
Team A has won 9 out of 14 games, so the probability of Team A winning is 9/14. Similarly, Team B has won 5 out of 14 games, so the probability of Team B winning is 5/14.
Now let's calculate the expected loss for each scenario:
1. If Team A wins:
- Bob wins the bet, receiving $10.
- You lose the bet, losing $4.
2. If Team B wins:
- You win the bet, receiving $10.
- Bob loses the bet, losing $6.
To calculate the expected loss, we multiply the outcome by its probability and sum them up:
Expected loss = (Probability of Team A winning * Money lost in that scenario) + (Probability of Team B winning * Money lost in that scenario)
Expected loss = ((9/14) * $4) + ((5/14) * $6)
Calculating this expression:
Expected loss ≈ ($2.57) + ($2.14)
Expected loss ≈ $4.71
Therefore, you can expect to lose approximately $4.71 on such a bet.