Multiple choice

A jar contains only green marbles, yellow marbles, and red marbles. If a marble is randomly selected from the jar, what is the probability that the marble will be either yellow or red? (1) The probability that the marble will be red is 0.3. (2) The probability that the marble will be green is 0.4.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The total probability is 1. P(Yellow) + P(Red) + P(Green) = 1. We want P(Yellow or Red) = 1 - P(Green). Statement (2) gives P(Green) = 0.4, so P(Yellow or Red) = 0.6. Statement (1) is insufficient on its own.

AI explanation

The probability of selecting either a yellow or red marble is the complement of selecting a green marble. Statement (2) alone provides the probability of selecting a green marble as 0.4, allowing us to find the target probability by subtracting 0.4 from 1 to get 0.6. Statement (1) only gives the probability of a red marble and lacks information about the yellow marbles, making it insufficient. Therefore, statement (2) alone is sufficient, but statement (1) alone is not sufficient.

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