Exam 13: Probability Rules

Jacob has a bag of his favorite marbles. It has 3 red marbles, 4 blue, and 10 of his most favorite color, neon orange. -If Jacob removes 3 marbles from the bag, what are the chances that he will get at least one orange?

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Question 1

Correct Answer:

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$P ( \text { at least one orange } ) = 1 - P ( \text { no orange } ) = 1 - \frac { 7 } { 17 } \cdot \frac { 6 } { 16 } \cdot \frac { 5 } { 15 } = 0.949$

Jacob has a bag of his favorite marbles. It has 3 red marbles, 4 blue, and 10 of his most favorite color, neon orange. -What is the probability that if he removes 2 marbles without looking, that he will get two orange marbles?

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Question 2

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$P ( 2 \text { orange marbles without replacement } ) = \frac { 10 } { 17 } \cdot \frac { 9 } { 16 } = \frac { 90 } { 272 } = 0.331$

Jacob has a bag of his favorite marbles. It has 3 red marbles, 4 blue, and 10 of his most favorite color, neon orange. -What is the probability that if a boat has chrome accents it is also made of natural wood?

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Question 3

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$\begin{array}{l}\begin{array} { | l | l | l | } \hline & \text { chrome } & \text { no chrome } \\\hline \text { wooden } & 0.70 & 0.20 \\\hline \text { not wooden } & 0.05 & 0.05 \\\hline\end{array}\\P ( \text { wood } \mid \text { chrome } ) = 0.70 / 0.75 = 93.3 \%\end{array}$

Jacob has a bag of his favorite marbles. It has 3 red marbles, 4 blue, and 10 of his most favorite color, neon orange. -Does it appear that having chrome accents and being made of wood are independent characteristics? Provide statistical evidence to justify your response.

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Question 4

Jacob has a bag of his favorite marbles. It has 3 red marbles, 4 blue, and 10 of his most favorite color, neon orange. -What are the chances that he as he removes marbles from the bag, he doesn't get an orange marble until his fourth attempt?

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Question 5

Jacob has a bag of his favorite marbles. It has 3 red marbles, 4 blue, and 10 of his most favorite color, neon orange. -If Jacob removes 3 marbles from the bag, what are the chances that he will get at least one orange?

Jacob has a bag of his favorite marbles. It has 3 red marbles, 4 blue, and 10 of his most favorite color, neon orange. -What is the probability that if he removes 2 marbles without looking, that he will get two orange marbles?

Jacob has a bag of his favorite marbles. It has 3 red marbles, 4 blue, and 10 of his most favorite color, neon orange. -What is the probability that if a boat has chrome accents it is also made of natural wood?

Jacob has a bag of his favorite marbles. It has 3 red marbles, 4 blue, and 10 of his most favorite color, neon orange. -Does it appear that having chrome accents and being made of wood are independent characteristics? Provide statistical evidence to justify your response.

Jacob has a bag of his favorite marbles. It has 3 red marbles, 4 blue, and 10 of his most favorite color, neon orange. -What are the chances that he as he removes marbles from the bag, he doesn't get an orange marble until his fourth attempt?

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