r

**Toolbox:**

- Let\(E_1\)=1 ball drawn is Blue B
- \(E_2\)=1 ball drawn is Red R
- A=2ball drawn
- P(A)=P\((E_1\) )P\((A/E_1\))+P\((E_2\))P\((A/E_2\))

P\((E_1\))=P(1ball drawn is B)

=\(\large\frac{5}{9}\)

P\((E_2\))=P(1ball drawn is R)

=\(\large\frac{4}{9}\)

P\((A/E_1\))=P(2nd ball drawn is blue given 1st ball dawn is blue)

=\(\large\frac{4}{8}\)

P\((A/E_2\))=P(2nd ball drawn is blue given 1st ball drawn is red)

=\(\large\frac{5}{8}\)

P(A)=\(\large\frac{5}{9}\times\)\(\large\frac{4}{8}\)+\(\large\frac{4}{8}\times\)\(\large\frac{5}{8}\)