Suppose a lottery ticket costs $1 and the probability that a holder will win nothing is 90%. What must the jackpot be for this to be a fair bet?Group of answer choices1,0001010,000100
Question
Suppose a lottery ticket costs $1 and the probability that a holder will win nothing is 90%. What must the jackpot be for this to be a fair bet?Group of answer choices1,0001010,000100
Solution
A fair bet is when the expected value of the bet is equal to the cost of the bet.
The expected value is calculated by multiplying each possible outcome by the probability of that outcome, and then summing these values.
In this case, there are two possible outcomes: winning the jackpot, and winning nothing.
The probability of winning nothing is 90%, or 0.9. Therefore, the probability of winning the jackpot is 10%, or 0.1.
Let's denote the jackpot as J.
The expected value of the bet is therefore 0.9 * $0 + 0.1 * J = 0.1J.
For the bet to be fair, the expected value must be equal to the cost of the bet, which is $1.
Therefore, we have the equation 0.1J = $1.
Solving for J, we get J = 10.
Therefore, the jackpot must be $10 for this to be a fair bet.
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