If there are four pens in a draw 2 red 1 green and 1 blue Tw

If there are four pens in a draw: 2 red, 1 green, and 1 blue. Two pens are drawn at random (without replacement). The events \"exactly one red\" and \"exactly one green\" are independent. True False

Solution

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Given 4 pens out of which 2 are Red, 1 Green and 1 Blue.

R1, R2, G ,B

Given 2 pens are drawn at random

Probability of drawing exactly 1 red pen

POSSIBLE CASES (R1G, R2G, R1B, R2B) = 4

SAMPLE SPACE (R1G, R2G, R1B, R2B, R1R2, GB) = 6

PROBABILITY = 4/6

Probability of drawing exactly one green pen =

POSSIBLE CASES (R1G, G2G, BG) = 3

PROBABIITY = 3/6

Clearly possible cases for both are over lapping hence the two events cannot be independent.

FALSE.