SOLUTION: A bag contains 7 red marbles, 9 white marbles, and 9 blue marbles. You draw 5 marbles out at random, without replacement. What is the probability that all the marbles are red? What
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-> SOLUTION: A bag contains 7 red marbles, 9 white marbles, and 9 blue marbles. You draw 5 marbles out at random, without replacement. What is the probability that all the marbles are red? What
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Question 1119875: A bag contains 7 red marbles, 9 white marbles, and 9 blue marbles. You draw 5 marbles out at random, without replacement. What is the probability that all the marbles are red? What is the probability that exactly two of the marbles are red? What is the probability that none of the marbles are red? Answer by ikleyn(52756) (Show Source):
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A bag contains 7 red marbles, 9 white marbles, and 9 blue marbles. You draw 5 marbles out at random, without replacement.
What is the probability that all the marbles are red?
What is the probability that exactly two of the marbles are red?
What is the probability that none of the marbles are red?
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Notice that the total number of marbles is 7 + 9 + 9 = 25.
Therefore the expressions for probabilities in all 3 cases have as the denominator.
(a) What is the probability that all the marbles are red?
You can select 5 red marbles of 7 red marbles in ways. Therefore the answer is .
(b) What is the probability that exactly two of the marbles are red?
You can select 2 red marbles of 7 red marbles in ways. Then you can add any 3 marbles of remaining 9+9 = 18 white and blue marbles.
You can do it in ways. Therefore the answer is ways.
(c) What is the probability that none of the marbles are red?
It means that you select 5 marbles among 18 = 9 + 9 white and blue marbles.
You can do it in ways. Therefore, the answer is .
Solved.
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In order for solve such problems with confidence and understand the solution, when it is presented to you, you should know the basics.
In this case, the basics is the info about Combinations.
