Question

Consider two options: (A) you receive a guaranteed payment of $100; (B) a coin is tossed and if heads comes up, you win nothing; if tails comes up, you win $200. The expected payoff for option B is:

Answer 1

• The expected payoff for option B is $100.

Step-by-step explanation:

The payoff is a random variable. The expected value, E(X), of a random variable is determined as the sum of the products of the value of each outcome by its corresponding probability:

`E(X)=\sum\limits^n_(i=1) {p(x_i)}\cdot x_i`

For option B:

• number of outcomes, n = 2 (head and tail)
• value of x₁ = head: 0
• probability of head, p(x₁) = 0.5
• value of x₂ = tail: $200
• parobablity of tail, p(x₂) = 0.5

`E(X)=0.5* 0+0.5* \$200=\$100`

Hence, the expected pay off is $100.