# Conditional probability

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**Probability Tree Diagram**

Bag A contains 2 red balls and 3 green balls. Bag B contains 1 red ball and 4 green balls.

A fair die is rolled: if a 1 or 2 comes up, a ball is randomly selected from Bag A;

if a 3, 4, 5, or 6 comes up, a ball is randomly selected from Bag B.

- It is known that 60% of graduating students are girls. Two grads are chosen at random. Given that at least one of the two grads are girls, determine the probability that both grads are girls.