Asked by Yazzy-pooh Mcguire on Sep 24, 2024
Verified
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
Coin Toss
A random method used to determine a decision, consisting of throwing a coin into the air and checking which side is facing up when it lands.
Expected Value
A statistical concept that calculates the average outcome of a probability event or investment over the long term.
- Grasp fundamentally the principle of expected value and the process of its calculation in elementary situations.
Verified Answer
HD
Hishor Dharsan.S5 days ago
Final Answer :
C
Explanation :
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.
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.
Learning Objectives
- Grasp fundamentally the principle of expected value and the process of its calculation in elementary situations.