May selects a marble from a jar containing 6 red marbles and 2 green marbles, and does not replace it. She then selects a second marble and does not replace it. She then selects a third marble. What is the probability that all three marbles will be red?

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Answer 1 · 2018-02-03T11:41:02

#5/14~=35.7%#

To get all three draws to be red, we first need to look at each individual draw:

First draw

There are 6 red and 2 green. The probability of drawing red is:

#6/8=3/4#

Second draw

There are now 5 red and 2 green. The probability of drawing red is:

#5/7#

Third draw

There are now 4 red and 2 green. The probability of drawing red is:

#4/6=2/3#

Putting it together

The probability of all three draws giving red marbles is:

#3/4xx5/7xx2/3=5/14~=35.7%#