Answer:
The contestant should try and answer question 2 first to maximize the expected reward.
Explanation:
Let the probability of getting question 1 right = P(A) = 0.60
Probability of not getting question 1 = P(A') = 1 - P(A) = 1 - 0.60 = 0.40
Let the probability of getting question 2 right be = P(B) = 0.80
Probability of not getting question 2 = P(B') = 1 - P(B) = 1 - 0.80 = 0.20
To obtain the better option using the expected value method.
E(X) = Σ xᵢpᵢ
where pᵢ = each probability.
xᵢ = cash reward for each probability.
There are two ways to go about this.
Approach 1
If the contestant attempts question 1 first.
The possible probabilities include
1) The contestant misses the question 1 and cannot answer question 2 = P(A') = 0.40; cash reward associated = $0
2) The contestant gets the question 1 and misses question 2 = P(A n B') = P(A) × P(B') = 0.6 × 0.2 = 0.12; cash reward associated with this probability = $200
3) The contestant gets the question 1 and gets the question 2 too = P(A n B) = P(A) × P(B) = 0.6 × 0.8 = 0.48; cash reward associated with this probability = $300
Expected reward for this approach
E(X) = (0.4×0) + (0.12×200) + (0.48×300) = $168
Approach 2
If the contestant attempts question 2 first.
The possible probabilities include
1) The contestant misses the question 2 and cannot answer question 1 = P(B') = 0.20; cash reward associated = $0
2) The contestant gets the question 2 and misses question 1 = P(A' n B) = P(A') × P(B) = 0.4 × 0.8 = 0.32; cash reward associated with this probability = $100
3) The contestant gets the question 2 and gets the question 1 too = P(A n B) = P(A) × P(B) = 0.6 × 0.8 = 0.48; cash reward associated with this probability = $300
Expected reward for this approach
E(X) = (0.2×0) + (0.32×100) + (0.48×300) = $176
Approach 2 is the better approach to follow as it has a higher expected reward.
The contestant should try and answer question 2 first to maximize the expected reward.
Hope this helps!!!