Question

A bag contains $4$ red and $5$ black balls, a second bag contain $3$ red and $7$ black balls. One ball is drawn at random from each bag, find the probability that the ball are of the same colour.

Answer 1

Let, R shows red ball and B shows black balls.

For $1^{st}$ bag:

Probability of getting red ball $P\left(R_1\right)=\frac{4}{9}$

Probability of getting black ball $P\left(B_1\right)=\frac{5}{9}$

For $2^{nd}$ bag:

Probability of getting red ball $P\left(R_2\right)=\frac{3}{10}$

Probability of getting black ball $P\left(B_2\right)=\frac{7}{10}$

Required probability $P$ : Balls drawn from both bags are of same colour.

That means either both balls are red or both are black.

Since, removal of ball from balls are independent events

,

$\Rightarrow P:P\left(R_1\right)P\left(R_2\right)+P\left(B_1\right)P\left(B_2\right)$

$\Rightarrow P:\frac{4}{9}\times \frac{3}{10}+\frac{5}{9}\times \frac{7}{10}$

$\Rightarrow P:\frac{12}{90}+\frac{35}{90}$

$\Rightarrow P:\frac{47}{90}$