A box has 5 blue and 4 red balls. One ball is drawn at random and not replaced. Its colour is also not noted. Then another ball is drawn at random. What is the probability of second ball being blue

The total number of balls initially in the box is 9, consisting of 5 blue and 4 red balls. The probability that the second ball drawn is blue depends on whether the first ball was blue or red: P(Blue first and Blue second) = (5/9) * (4/8) = 20/72, and P(Red first and Blue second) = (4/9) * (5/8) = 20/72. Using the law of total probability by adding these two probabilities gives 20/72 + 20/72 = 40/72, which simplifies to 5/9.

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