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Sagot :
Part (A)
We have 6 red and 4 blue marbles, so 6+4 = 10 total.
The probability of getting red is 6/10 since we have 6 red out of 10 total.
The probability of getting another red is 5/9 because we don't put the first marble back.
The probability of getting two reds in a row is (6/10)*(5/9) = 30/90 = 1/3
Answer: 1/3
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Part (B)
4/10 represents the probability of getting blue on the first try
3/9 represents the probability of getting a blue marble on the second try
We don't put the marble back.
(4/10)*(3/9) = 12/90 = 4/30 is the probability of getting two blues in a row.
Answer: 4/30
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Part (C)
Add up the results of parts (A) and (B)
1/3 + 4/30
10/30 + 4/30
(10+4)/30
14/30
7/15
The result 7/15 is the probability of either getting two reds OR getting two blues (pick one case only). This tells us that 7 out of 15 times we'll have this happen. This must mean the remaining 8 times will have two marbles of different colors.
So 8/15 is the probability of picking one marble of each color.
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As an alternative, we could also consider it like this
(6/10)*(4/9) = 24/90 = 4/15
This represents the probability of picking red first, then blue next.
Similarly,
(4/10)*(6/9) = 24/90 = 4/15
represents the probability of picking blue first, then red next.
Therefore, 4/15+4/15 = 8/15 is the probability of getting one of each color.
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Answer: 8/15
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