Question

A bag contains 5 red abd 4 black balls .a ball is drawn at random from the vag and pyt into another bag which contains 3 red and 7 black balls. a ball is frawn ranfomly from the second bag.what is the probb that it is red

Answer 1

4/11 hope it is helpful

Answer 2

Let event E1: Red ball is drawn from the first bag and event E2: Black ball is 

drawn from the first bag.

P(E1) = 5/9 P(E2) = 4/9

(Note that E1 and E2 are exhaustive events and mutually exclusive)

Let event A:  Red ball is drawn from the second bag.

P(A /E1) = P(Red ball is drawn from the second bag under the condition that 

black ball is transferred from the first bag to the second bag) = 3/10

Similarly, 

P(A/E2) = P(Red ball is drawn from the second bag under the condition that red 

ball is transferred from the first bag to the second bag) = 4/10

Therefore, required probability= P (red ball is drawn from the second bag)

P (A) = P (A∩E1) + P (A∩E2)

= P (E1) × P (A/E1) +P(E2) × P(A/E2)

= 5/9 × 3/10 + 4/9 × 4/10

= 15/90 + 16/90

= 31/90

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