A toy store sells individual marbles in a variety of colors and sizes.Red Green PurpleBig 5 8 2Small 4 6 9What is the probability that a randomly selected marble is purple or is not small?Simplify any fractions.Submit
Question
A toy store sells individual marbles in a variety of colors and sizes.Red Green PurpleBig 5 8 2Small 4 6 9What is the probability that a randomly selected marble is purple or is not small?Simplify any fractions.Submit
Solution
To solve this problem, we first need to calculate the total number of marbles. We do this by adding up all the numbers in the table:
5 (big red) + 8 (big green) + 2 (big purple) + 4 (small red) + 6 (small green) + 9 (small purple) = 34 marbles in total.
Next, we calculate the number of marbles that are purple or not small.
The number of purple marbles (big or small) is 2 (big purple) + 9 (small purple) = 11.
The number of marbles that are not small (i.e., big) is 5 (big red) + 8 (big green) + 2 (big purple) = 15.
However, we have counted the big purple marbles twice (once for being purple and once for being big), so we need to subtract the number of big purple marbles from our total.
So, the number of marbles that are purple or not small is 11 (purple) + 15 (not small) - 2 (big purple) = 24.
Finally, we calculate the probability by dividing the number of desired outcomes (marbles that are purple or not small) by the total number of outcomes (total marbles):
Probability = 24 / 34 = 12 / 17.
So, the probability that a randomly selected marble is purple or is not small is 12/17.
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