Question
A model suggests: if a trade wins, next trade wins with 70% chance. If a trade loses, next trade wins with 40%. First trade wins. What is the probability second and third both win?
Check your answer
Solution
Answer: 0.49
Given the conditional probabilities
\[
P(W_2 \mid W_1) = 0.7 \quad \text{and} \quad P(W_3 \mid W_2) = 0.7,
\]
the chain rule tells us that the joint probability \( P(W_3, W_2 \mid W_1) \) can be found by multiplying these conditionals:
\[
P(W_3, W_2 \mid W_1) = P(W_2 \mid W_1) \times P(W_3 \mid W_2) = 0.7 \times 0.7 = 0.49.
\]