SOLUTION: Two marbles are drawn randomly one after the other without replacement from a jar that contains 9 red marbles, 9 white marbles, and 3 yellow marbles. Find the probability of the fo

Question 1197574: Two marbles are drawn randomly one after the other without replacement from a jar that contains 9 red marbles, 9 white marbles, and 3 yellow marbles. Find the probability of the following events.
(a) A red marble is drawn first followed by a white marble.
The probability is:
(b) A white marble is drawn first followed by a white marble.
The probability is:
(c) A yellow marble is not drawn at all.
The probability is:
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

These are very basic probability problems. You need to know two things:

(1) The probability of an event with discrete outcomes is the ratio of the number of "good" outcomes to the total number of possible outcomes.

(2) The probability of a particular sequence of outcomes is the product of the probabilities of each.

(a) A red marble is drawn first followed by a white marble.
Tranlsation: A red marble first AND a white marble second.
P(red marble first): 9+9+3=21 marbles, 9 red marbles, so 9/21 = 3/7
P(white marble second): 8+9+3=20 marbles, 9 white marbles, so 9/20
P(red then white) = (3/7)(9/20) = 27/140

(b) A white marble is drawn first followed by a white marble.
Tranlsation: A white marble first AND a white marble second.
P(white marble first): 9+9+3=21 marbles, 9 white marbles, so 9/21 = 3/7
P(white marble second): 9+8+3=20 marbles, 8 white marbles, so 8/20 = 2/5
P(white then white) = (3/7)(2/5) = 6/35

(c) A yellow marble is not drawn at all.
Tranlsation: A red or white marble first AND a red or white marble second.
P(red or white marble first): 9+9+3=21 marbles, 9+9=18 red or white marbles, so 18/21 = 6/7
P(red or white marble second): 9+8+3=20 marbles, 9+8=17 red or white marbles, so 17/20
P(red or white then red or white) = (6/7)(17/20)=51/70

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