SOLUTION: A jar contains 10 blue marbles, 5 red marbles, 4 green marbles, and 1 yellow marble. Two marbles are chosen (without replacement). Please show work. (a) What is the probability th

Algebra ->  Probability-and-statistics -> SOLUTION: A jar contains 10 blue marbles, 5 red marbles, 4 green marbles, and 1 yellow marble. Two marbles are chosen (without replacement). Please show work. (a) What is the probability th      Log On


   

Question 1027435: A jar contains 10 blue marbles, 5 red marbles, 4 green marbles, and 1 yellow marble. Two marbles are chosen (without replacement). Please show work.
(a) What is the probability that one will be green and the other red?
(b) What is the probability that one will be blue and the other yellow?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You could choose either green then red or red then green so calculate both ways and add.
Green first, red second: P%28G%29=4%2F%2810%2B5%2B4%2B1%29=4%2F20=1%2F5
P%28R%29=5%2F19
P%28G%2CR%29=%281%2F5%29%285%2F19%29=1%2F19
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Red first, green second: P%28R%29=5%2F20=1%2F4
P%28G%29=4%2F19
P%28G%2CR%29=%281%2F4%29%284%2F19%29=1%2F19
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So then,
P=1%2F19%2B1%2F19=2%2F19
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Similarly,
Blue first, yellow second: P%28B%29=10%2F20=1%2F2
P%28Y%29=1%2F19
P%28B%2CY%29=%281%2F2%29%281%2F19%29=1%2F38
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Yellow first, blue second: P%28Y%29=1%2F20
P%28B%29=10%2F19
P%28Y%2CB%29=%281%2F20%29%2810%2F19%29=1%2F38
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So then,
P=1%2F38%2B1%2F38=1%2F19