SOLUTION: A vase contains 7 red and 3 blue marbles. 3 marbles are drawn at random without replacement. Find the probability of drawing the first 2 as red and the third marble as blue
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Question 237221: A vase contains 7 red and 3 blue marbles. 3 marbles are drawn at random without replacement. Find the probability of drawing the first 2 as red and the third marble as blue
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
You can think of this as three independent drawings, and calculate each probability GIVEN that the previous drawings have taken place. The probability is then the PRODUCT of these three probabilities.
The probability of drawing a red marble on the first draw is 7/10.
The probability of drawing a red marble on the second draw given that the first draw was red is 6/9, since there are 6 red marbles left out of 9 total marbles.
The probability of drawing a blue marble on the THIRD draw given that the first two marbles were red (remember now that 2 reds were removed, leaving all 3 blue marbles out of 8 remaining marbles!) will be 3/8.
Total probability =
=
=
Reduce the fraction by dividing out a 6:
=
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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