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In the following question, 3 statements are given. You have to find which is/are necessary and sufficient to answer the following question. Two containers each contain some balls of Red and Blue color. Now all the balls of these two containers are mixed into a single third container which also contained some Red and Blue color balls initially as well. If 5 balls are taken out, then find the probability that all the balls taken out are Red in color. Statement 1∶ Total number of balls finally in 3rd container is 135. Statement 2∶ Ratio of balls in 1st container and 2nd container is 2 ∶ 7 Statement 3∶ Ratio of Red and Blue balls in 3rd container before mixing is 2 ∶ 3

In the following question, 3 statements are given. You have to find which is/are necessary and sufficient to answer the following question. Two containers each contain some balls of Red and Blue color. Now all the balls of these two containers are mixed into a single third container which also contained some Red and Blue color balls initially as well. If 5 balls are taken out, then find the probability that all the balls taken out are Red in color. Statement 1∶ Total number of balls finally in 3rd container is 135. Statement 2∶ Ratio of balls in 1st container and 2nd container is 2 ∶ 7 Statement 3∶ Ratio of Red and Blue balls in 3rd container before mixing is 2 ∶ 3 Correct Answer All the statements are not sufficient to answer the question.

Ratio of balls in 1st container and 2nd container is 2 ∶ 7

Let balls in 1st container = 2x

Balls in 2nd container = 7x

Total balls of 1st and 2nd container mixed in 3rd container = 2x + 7x = 9x

Ratio of red balls and blue balls in 3rd container before mixing = 2 ∶ 3

Red balls = 2y and Blue balls = 3y , total balls in 3rd container already is = 5y              

Total balls after mixing in 3rd container is = 9x + 5y

∴ No relation between the red balls and blue balls of 1st and 2nd container is given, and we cannot infer answer from the given statements.

∴ All the statements are not sufficient to answer the question.

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