In a coin toss bet,where both heads and tails are equally likely,you win a $3 on heads but lose $1 on tails.The expected value of the bet is
A)$0.50
B)-$0.50
C)$1.00
D)$0.00

Question

​In a coin toss bet,where both heads and tails are equally likely,you win a $3 on heads but lose $1 on tails.The expected value of the bet is
A)​$0.50
B)-$0.50
C)$1.00
D)​$0.00

Quizplus · Accepted Answer

To find the expected value of the bet, we multiply the probability of each outcome by the payout (or loss) for that outcome and sum them up.

Let H be the event of getting heads, and let T be the event of getting tails.

P(H) = P(T) = 1/2 (since both are equally likely)

So, the expected value of the bet is:

E(X) = P(H)*$3 + P(T)*(-$1)

E(X) = 1/2 * $3 + 1/2 * (-$1)

E(X) = $1.50 - $0.50

E(X) = $1.00

Since the expected value is positive, we should choose to make the bet. This means that in the long run, we can expect to make a profit of $1 for every bet we make.

​In a Coin Toss Bet,where Both Heads and Tails Are

In a Coin Toss Bet,where Both Heads and Tails Are