Suppose Shristi owns a house that is worth $490,000 located in a fire hazard zone. There is a 2% (or 0.02) chance that her house will catch a fire in which case it will be completely destroyed (and 98% or 0.98 chance that it will remain intact). What is the expected value of her house?

Question

Suppose Shristi owns a house that is worth $490,000 located in a fire hazard zone.  There is a 2% (or 0.02) chance that her house will catch a fire in which case it will be completely destroyed (and 98% or 0.98 chance that it will remain intact). What is the expected value of her house?

BlackTom AI · Accepted Answer

The problem asks for the expected value of Shristi's house given two possible outcomes and their probabilities.

Step 1: Identify outcomes and probabilities. The house is destroyed with probability 0.02, yielding a value of $0. The house remains intact with probability 0.98, yielding its full value of $490,000.

Step 2: Apply the expected value formula. EV = (probability of outcome 1 × value of outcome 1) + (probability of outcome 2 × value of outcome 2).

Step 3: Compute each term. For destruction: 0.02 × 0 = 0. For intact: 0.98 × 490,000 = 490,000 − (0.02 × 490,000) = 490,000 − 9,800 = 480,200.

Step 4: Sum the terms. EV = 0 + 480,200 = 480,200.

Step 5: Interpret the result. The expected value represents the long-run average value per such house if this risk scenario were repeated many times; on average, each house would contribute $480,200 to the expected value over many trials.

Note: There are no multiple-choice options provided to evaluate here; the calculation follows directly from the two possible outcomes and their probabilities.

COMM_V 295 105 106 2025W1 Participation/Math Quiz #3

Suppose Shristi owns a house that is worth $490,000 located in a fire hazard zone. There is a 2% (or 0.02) chance that her house will catch a fire in which case it will be completely destroyed (and 98% or 0.98 chance that it will remain intact). What is the expected value of her house?

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COMM_V 295 105 106 2025W1 Participation/Math Quiz #3

Suppose Shristi owns a house that is worth $490,000 located in a fire hazard zone. There is a 2% (or 0.02) chance that her house will catch a fire in which case it will be completely destroyed (and 98% or 0.98 chance that it will remain intact). What is the expected value of her house?

View Explanation

Log in for full answers

Similar Questions

The expected value of a "strange die" that has the values {2,3,4,6,7,8} the expected value is ... _________________________________________________________ in case you ask, a "normal" die is this, giving values 1 to 6.

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Let p=0.31 and q=0.81. Then, we we have E(X)=12.9, E(Y)=1.589, Var(X)=13.3651 and Var(Y)=60.59. What is E(4*X-9*Y)?

For some values of p and q, the payoff associated with sensing consolation is 250, and the payoff associated with sensing desolation is 200. What is the payoff associated with taking the personal retreat?

As a birthday gift, you are mailing a new personal digital assistant (PDA) to your cousin in Toledo. The PDA cost $446. There is a 4 percent chance it will be lost or damaged in the mail. Is it worth $4 to insure the mailing?

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Let p=0.31 and q=0.81. Then, we we have E(X)=12.9, E(Y)=1.589, Var(X)=13.3651 and Var(Y)=60.59. What is E(4X-9Y)?