A bag of 11 marbles contains 6 marbles with red on them, 6 with blue on them, 6 with green on them, and 2 with red and green on them. What is the probability that a randomly chosen marble has either green or red on it? Note that these events are not mutually exclusive. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

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28-10-2022
Mathematics

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A bag of 11 marbles contains 6 marbles with red on them, 6 with blue on them, 6 with green on them, and 2 with red and green on them. What is the probability that a randomly chosen marble has either green or red on it? Note that these events are not mutually exclusive. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

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ArielyP201778 ArielyP201778 · Answer 1 · 2022-10-28T16:07:09-04:00

[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ P(A)=Probability\text{ marble has gre}en \\ P(B)=Probability\text{ marble has red} \\ P(A\cap B)=Probability\text{ marble has gre}en\text{ and red} \\ P(A)=\frac{6}{11} \\ P(B)=\frac{6}{11} \\ P(A\cap B)=\frac{2}{11} \\ P(A\cup B)=\frac{6}{11}+\frac{6}{11}-\frac{2}{11} \\ P(A\cup B)=\frac{10}{11} \\ \text{The probability of chosen a marble that has either gr}een\text{ } \\ \text{or red on it is }\frac{10}{11} \end{gathered}[/tex]