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.

Explanation

According to question,

`Rightarrow` Bag A=(4 R+5 B) balls

`Rightarrow` Bag B =(3 R+7 B) balls

`Rightarrow` Probability of both are red balls `=frac{4}{9} times frac{3}{10}=frac{12}{90}`

`Rightarrow` Probability of both are black balls `=frac{7}{10} times frac{5}{9}=frac{35}{90}`

`Rightarrow` P(balls of same colours )=P( Both red )+P (Both black)


`=frac{12}{90}+frac{35}{90}`/

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