Question

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?

Answer 1

Given that 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 first ball drawn is red

And E is the event that second ball drawn is blue.

∴ P(E) = `"P"("E"_1)."P"("E"/"E"_1) + "P"("E"_2)."P"("E"/"E"_2)`

= `5/9 xx 4/8 + 4/9 xx 5/8`

= `20/72 + 20/72`

= `40/72`

= `5/9`

Hence, the required probability is `5/9`.