A box contains balls that are either yellow, black, or brown in color. One ball is chosen at random from the box. Is the

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A box contains balls that are either yellow, black, or brown in color. One ball is chosen at random from the box. Is the probability that the chosen ball is black greater than \(\dfrac34?\)

(1) The probability that the chosen ball is not brown is less than \(\dfrac25.\)
(2) The probability that the chosen ball is not black is greater than \(\dfrac35.\)

Answer: D

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Target question: Is the probability that the chosen ball is black greater than 3/4?
I.e Is the probability of choosing black ball = 3/4?
Statement 1: The probability that the chosen ball is not brown is less than 2/5.
If the ball is not brown, then it is black or yellow.
Therefore, the probability of choosing black or yellow => probability of choosing black + probability of choosing yellow < 2/5
Probability of choosing black ball < 2/5 - probability of choosing yellow
Probability of choosing black ball < 2/5. Since 2/5 < 3/4, the probability of blackball being chosen is 3/4. So, definitely, the probability of choosing a black ball is < 3/4. Hence, statement 1 is SUFFICIENT.

Statement 2: The probability that the chosen ball is not black is greater than 3/5.
1 - probability of choosing black ball > 3/5
1 - 3/5 > probability of choosing a black ball
2/5> probability of choosing a black ball
I.e probability of choosing a black ball < 2/5. Since 2/5 is less than 3/4, then, the probability of choosing a black ball is < 3/4. Statement 2 is also SUFFICIENT.
Since each statement alone is SUFFICIENT, the answer is, therefore, equal to option D.