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  • 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?

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?

Answers (1)

Given-

The box has 5 blue and 4 red balls.

Let E1 be the event that first ball drawn is blue

E2 be the event that the first ball drawn is red and

E be the event that second ball drawn is blue.

\\ P\left(E_{1}\right)=\frac{5}{9} \\ P\left(E_{2}\right)=\frac{4}{9} \\ P\left(E \mid E_{1}\right)=\frac{4}{8} \\ P\left(E \mid E_{2}\right)=\frac{5}{8} \\ \therefore P(E)=P\left(E_{1}\right) . P\left(E \mid E_{1}\right)+P\left(E_{2}\right) \cdot P\left(E \mid E_{2}\right) \\ =\frac{5}{9} \times \frac{4}{8}+\frac{4}{9} \times \frac{5}{8} \\ =2\left(\frac{20}{72}\right) \\ =\frac{40}{72} \\ =\frac{5}{9}

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infoexpert22

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