Picture a seesaw: on one side, losing $5 (60% chance), on the other, gaining $5 (40% chance). The seesaw tilts left, meaning on average, Jordan loses $1 per game! So, skip the shot and save your cash, Jordan!
Here's how to figure out whether Jordan should play the carnival basketball game:
Miss both: Lose $5 (pay $5 entry fee, gain nothing).
Make one: Break even (get $5 back for the entry fee).
Make both: Profit $5 (get $10 back, minus the $5 entry fee).
Multiply each outcome by its probability:
Miss both: (-$5) * (60% chance) = -$3
Make one: ($0) * (40% chance) = $0
Make both: ($5) * (40% chance) = $2
Add the weighted outcomes: -$3 + $0 + $2 = -$1
Since Jordan's expected outcome is negative $1, he should not play the game. On average, he'll lose money in the long run.
Remember:
This analysis assumes Jordan plays the game many times. In a single game, any outcome is possible.
Jordan's skill in making shots can affect the probabilities and change the expected outcome.
So, while the game might be tempting, the odds aren't in Jordan's favor. He's better off saving his money or trying a different game at the carnival.
Imagine a seesaw where the left side represents losses (-$5) and the right side represents gains ($5). The probability of each outcome acts as the weight on each side. If the left side weighs down more (like in this case), playing the game is not advantageous.