In a jar are 10 marbles: 4 red, 5 blue, and 1 yellow. Why can we use the special addition rule to calculate the probability that a single marble drawn from the jar will be either red or yellow? What is the probability?

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In a jar are 10 marbles: 4 red, 5 blue, and 1 yellow. Why can we use the special addition rule to calculate the probability that a single marble drawn from the jar will be either red or yellow? What is the probability?

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Answer 1 · 2015-01-01T04:19:24

$\frac{1}{2}$ $1/2$

The general addition rule states that:

$P (A or B) = P (A) + P (B) - P (A and B)$ $P(A or B) = P(A) + P(B) - P(A and B)$

However, in cases where two events are mutually exclusive, such as different colors of solid marbles on a single draw, then $P (A and B) = 0$ $P(A and B) = 0$ , so:

$P (A or B) = P (A) + P (B)$ $P(A or B) = P(A) + P(B)$

In this case, $P (red or yellow) = \frac{4}{10} + \frac{1}{10} = \frac{5}{10} = \frac{1}{2}$ $P("red" or "yellow") = 4/10 + 1/10 = 5/10 = 1/2$

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In a jar are 10 marbles: 4 red, 5 blue, and 1 yellow. Why can we use the special addition rule to calculate the probability that a single marble drawn from the jar will be either red or yellow? What is the probability?

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