You have a 60% chance to win a game. If you play twice, what is the probability of winning both games?

Instruction: Assume the two game outcomes are independent and each has a 60% win probability. Calculate the chance of winning both, and explain where independence is used.

Context: This question assesses the candidate's understanding of independent events and their probabilities.

Updated

Official answer

For independent games with win probability 0.6 each, P(win both) = 0.6 × 0.6 = 0.36, or 36%.

The general rule is P(W1 and W2) = P(W1)P(W2 | W1). Independence permits replacing the conditional probability with 0.6. Equal marginal chances alone are insufficient: if both games always have the same outcome, the probability of winning both would be 0.6 instead.

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