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## Comment on

Green or Ball## I know the probability of a

## P(green object) = 1/4 and P

P(green object) = 1/4 and P(ball) = 2/3

However, P(green and ball) = (1/4)(2/3) = 1/6 ONLY IF these two events (being green and being a ball) are independent. In this case, they clearly aren't independent since we're told that P(green and ball) = 1/5 (and not 1/6)

For more on independence see: https://www.greenlighttestprep.com/module/gre-probability/video/755 and https://www.greenlighttestprep.com/module/gre-probability/video/756

## A bit of a confusing question

The question could be better clarified by asking, "What is the probability of selecting an object that is green or a ball, but not both?"

## My calculations for P(green

My calculations for P(green or ball) INCLUDE the scenario that the object is green AND a ball.

I think the "or" probability formula is throwing you off, since it subtracts "P(green and ball)" at the end. However, this does not mean that we are saying that an object that is both a ball and green does not meet the conditions. We subtract "P(green and ball)" at the end in order to remove duplication in our calculations.

For more on why we need to subtract PA AND B), watch this earlier video: https://www.greenlighttestprep.com/module/gre-probability/video/748

## In this question, why can't

P(green ball) = P(green)*P(ball)

1/5 = P(green)*2/3

P(green) = 3/10

## That formula would be used if

That formula would be used if we were looking for the probability that the selected item is green AND is a ball. Also, the this approach would be valid ONLY IF the two events were independent (which they are not).

## The probability of selecting

## The box contains balls AND

The box contains balls AND chips. Some BALLS are green and some CHIPS are green.

P(green) refers to the probability that we select EITHER a green ball OR a green chip.

So, knowing that P(selecting a green ball) = 1/5 is not enough to determine P(green). We must also consider P(selecting a green CHIP)

Does that help?

Cheers,

Brent

## Thanks. It is clear after

## can a chip be colored to be

## The question tells us that

The question tells us that each OBJECT is red, blue or green. Since each object can be a ball or a chip, it's possible to have red balls AND red chips.

Cheers,

Brent