Question

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 NOT true?

A.The probability of both events happening is 50%.

B.The probability of either of these events happening is 33%.

C.Event 1 is independent of Event 2.

D.The probability of Event 1 occurring is the same as the probability of Event 2 occurring.

Answer 1

There 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 B).

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

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

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

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

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

Also, P(A B) P(A) P(B).

So, A and B are not independent.

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