Answer:
Step-by-stPart A
Answer: 7/36
This is in fraction form
The decimal version of this number is roughly 0.1944
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To get this answer, we multiply the fractions 7/9 and 2/8
The fraction 7/9 is the probability of selecting purple on the first draw. There are 7 purple out of 9 total (2+7 = 9)
The fraction 2/8 is the probability of selecting white on the second draw. This is assuming we don't put the first selection back in the bag. There are 2 white out of 8 marbles over
Multiply the fractions to get:
(7/9)*(2/8) = (7/9)*(1/4) = (7*1)/(9*4) = 7/36
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Part B
Answer in fraction form: 1/36
Answer in decimal form: 0.0278 (which is approximate)
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We have 2 white out of 9 total. So the probability of getting white the first time is 2/9
After we select and don't put that first selection back, we have 1 white out of 8 left over. The probability of getting white a second time is 1/8
Multiply the fractions:
(2/9)*(1/8) = (2*1)/(9*8) = 2/72 = 1/36
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Part C
Answer: There is a greater chance to get two purple in a row
Without doing any math, you can tell that purple is more likely simply because there are more purple than white. We have 7 purple and 2 white. For any given single selection, we have a greater chance of picking purple over white.
If you want do to the math, then the probability of selecting two white marbles in a row is 1/36 = 0.0278 which was found in part B above.
The probability of selecting two purple is (7/9)*(6/8) = (7/9)*(3/4) = (7*3)/(9*4) = 21/36 = 7/12 = 0.5833
In summary,
the probability of selecting two white marbles in a row is 0.0278
the probability of selecting two purple marbles in a row is 0.5833
we see that the probability for the two purple marbles is much greater
