You have placed a wager such that you will either receive nothing if you lose the bet or you will receive $10 if you win the bet. If the expected cash receipt of the wager is $9, then there is a 100 per cent probability that you will win the wager.

Question

Quizplus · Accepted Answer

The expected cash receipt is equal to the probability of winning multiplied by the amount won, plus the probability of losing multiplied by the amount lost. Let's call the probability of winning "p". Then we can set up the equation:
$9 = p(10) + (1-p)(0)$
Simplifying the equation, we get:
$9 = 10p$
$p = 0.9$
This means that there is a 90% probability of winning, not a 100% probability as stated in the statement. Therefore, the correct answer is B, false.

You Have Placed a Wager Such That You Will Either