A bucket contains exactly 3 marbles, one red, one blue and one green. A person arbitrarily pulls out each marble one at a time. Given the following: Event 1: The first marble removed is non-red Event 2: The last marble removed is non-red Which of the following statements is true? Group of answer choices The probability of either of these events happening is 33%. The probability of Event 1 occurring is the same as the probability of Event 2 occurring. Event 1 is independent of Event 2. The probability of both events happening is 50%.

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Step-by-step explanation:

here are 6 possible sequences of removing 3 marbles. Let R be the red marble, B be the blue marble and G be the green marble. The possible sequences are: RBG, RGB, BGR, BRG, GRB and GBR.

Let A denotes Event 1 and B denotes Event 2.

The favorable cases for A are: BGR, BRG, GRB and GBR.

So, P (A) = 4/6 = 2/3.

The favorable cases for B are: RBG, RGB, BRG and GRB.

So, P (B) = 4/6 = 2/3.

The probability of both events happening is P (A / cap B).

Favorable cases for (A / cap B) are BRG and GRB.

Thus, P (A / cap B) = 2/6 = 1/3.

The probability of either of these events happening is P (A / cup B).

Favorable cases for (A / cup B) are RBG, RGB, BRG, BGR, GRB and GBR.

Thus, P (A / cup B) = 6/6 = 1.

Also, P (A / cap B) / neq P (A) P (B).

So, A and B are not independent.

Hence, Option (D) is the only true statement. (Ans).