Answer:
- The expected payoff for option B is $100.
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:
[tex]E(X)=\sum\limits^n_{i=1} {p(x_i)}\cdot x_i[/tex]
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
[tex]E(X)=0.5\times 0+0.5\times \$200=\$100[/tex]
Hence, the expected pay off is $100.
