Problem 22
You have the correct answer since there are 9 non-white socks out of 15 total.
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Problem 23
Answer: A) 7/20
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Step-by-step explanation:
We have 10 blue marbles and 10+4+5+6 = 14+11 = 25 marbles total
This means there are 25-10 = 15 non-blue marbles.
The probability of selecting a non-blue marble is 15/25. I won't reduce this as we'll use this fraction to set up the next probability.
Because the marble is not replaced, this means we go from 15 non-blue marbles to 15-1 = 14 non-blue marbles. We also go from 25 total marbles to 25-1 = 24 total.
In short, the fraction 15/25 turns into 14/24 after subtracting 1 from each part.
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Let's reduce each fraction mentioned
15/25 = (3*5)/(5*5) = 3/5
14/24 = (2*7)/(2*12) = 7/12
Then we'll multiply the two reduced fractions
(3/5)*(7/12) = (3*7)/(5*12) = 21/60
Lastly, we'll reduce that result
21/60 = (3*7)/(3*20) = 7/20
The probability of selecting two marbles that aren't blue is 7/20. This is done without replacement.
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As a shortcut, we could say:
(15/25)*(14/24) = 7/20