A student calculates P(two blue) when drawing two balls without replacement from a bag with 4 blue and 6 red balls. They get 4/10 × 4/10 = 16/100. What mistake have they made?

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Question

A student calculates P(two blue) when drawing two balls without replacement from a bag with 4 blue and 6 red balls. They get 4/10 × 4/10 = 16/100. What mistake have they made?

Accepted Answer

B) They used the probability with replacement instead of without replacement — Without replacement, after one blue ball is taken, only 3 blue remain from 9 total, so P(blue second | blue first) = 3/9, not 4/10. The student has treated the events as independent (with replacement). This is a very common misconception.

Answer

D) They forgot to square the final answer

Answer

B) They used the probability with replacement instead of without replacement

Answer

C) They used the wrong colour's probability

Answer

A) They multiplied instead of adding the branch probabilities

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