SOLUTION: A bag contains 5 red balls and 3 blue balls. If two balls are drawn at random without replacement, what is the probability that both balls are red?
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-> SOLUTION: A bag contains 5 red balls and 3 blue balls. If two balls are drawn at random without replacement, what is the probability that both balls are red?
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Question 1206946: A bag contains 5 red balls and 3 blue balls. If two balls are drawn at random without replacement, what is the probability that both balls are red? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52756) (Show Source):
The response from the other tutor shows a solution using one standard method -- selecting the balls one at a time, finding the probability that each successive draw gets a red ball, and multiplying the two probabilities to get the final answer.
A student should know and understand that method for solving the problem.
The other basic method for solving the problem is using the basic definition of probability:
# of good outcomes
probability = ------------------------
# of possible outcomes
A good outcome is choosing 2 of the 5 red balls; the number of ways of doing that is "5 choose 2": C(5,2)=10.
The possible outcomes are choosing any 2 of the 8 balls; the number of ways of doing that is "8 choose 2": C(8,2)=28.
So, using the basic definition of probability, the probability of choosing 2 red balls is 10/28 = 5/14.
