Question 1189347: * Show your complete solution
* Explain your answer after the solution
Suppose box A contains 5 red and 3 white balls. If two balls are drawn in succession without replacement, what is the probability of getting
a. red on the first draw
b. red on the first and red on the second draws
c. white on the first and red on the second draws
d. white on the second given that it is white on the first
Answer by math_tutor2020(3817)   (Show Source):
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Part (a)
Answer: 5/8
Reason:
There are 5 red balls out of 8 balls total (5 red+ 3 white = 8 total)
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Part (b)
Answer: 5/14
Reason:
5/8 is the previous probability mentioned of getting red.
Assuming the ball is not put back, this means we have 4 red and 7 left over.
So 4/7 is the probability of getting another red.
Therefore, (5/8)*(4/7) = 20/56 = 5/14 represents getting two red in a row without replacement.
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Part (c)
Answer: 15/56
Reason:
3/8 is the probability of getting white on the first draw (3 white out of 8 total)
5/7 is the probability of getting red on the second draw, assuming the first ball is not put back.
Multiply the fractions mentioned
(3/8)*(5/7) = 15/56
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Part (d)
Answer: 2/7
Reason:
We're told that the first selection is white. So we have 3-1 = 2 white left out of 7 left over.
Therefore, 2/7 is the probability of getting a second white given the first is white.
We do not multiply like we did with parts (b) and (c), simply because we only have one fraction to work with here.
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