05 Introduction to Probability Part 1

# Probability that at least one red is drawn pa1pa2pa3

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Probability that at least one red is drawn P(a1)+P(a2)+P(a3) P (A) = 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 Second Draw First Draw red green yellow red green yellow 15

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Assigning probabilities to events For any event A P(A) = sum of the probabilities for the elementary outcomes in A If A = {a1,a2,a3} P(A) = Example: Drawing marbles A = event that at least one red is drawn B = event that two of the same color are drawn 1. Probability that at least one red is drawn P (A) = P(1 red) + P(2 reds) = 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 Second Draw First Draw red green yellow red green yellow 16 P(a1)+P(a2)+P (a3)
Assigning probabilities to events For any event A P(A) = sum of the probabilities for the elementary outcomes in A If A = {a1,a2,a3} P(A) = Example: Drawing marbles A = event that at least one red is drawn B = event that two of the same color are drawn 1. Probability that at least one red is drawn P (A) = P(1 red) + P(2 reds) = 4/9 +1/9 = 5/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 Second Draw First Draw red green yellow red green yellow 17 P(a1)+P(a2)+P (a3)

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Assigning probabilities to events For any event A P(A) = sum of the probabilities for the elementary outcomes in A If A = {a1,a2,a3} P(A) = Example: Drawing marbles A = event that at least one red is drawn B = event that two of the same color are drawn 1. Probability that at least one red is drawn P (A) = P(1 red) + P(2 reds) = 4/9 + 1/9 = 5/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 Second Draw First Draw red green yellow red green yellow 18 P(a1)+P(a2)+P (a3)
Assigning probabilities to events 2. Probability that two of the same color are drawn 3. P( A and B) 4. P(A or B) 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 Second Draw First Draw red green yellow red green yellow P (B) = P(rr) + P(gg) + P(yy) = 1/9 +1/9 +1/9 = 1/3 19

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Assigning probabilities to events 2. Probability that two of the same color are drawn 3. P( A and B) 4. P(A or B) 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 Second Draw First Draw red green yellow red green yellow P (B) = P(rr) + P(gg) +P(yy) = 1/9 +1/9 +1/9 = 1/3 20
Assigning probabilities to events 2. Probability that two of the same color are drawn 3. P( A and B) 4. P(A or B) 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 Second Draw First Draw red green yellow red green yellow P (B) = P(rr) + P(gg) +P(yy) = 1/9 +1/9 +1/9 = 1/3 P(A and B) = P(rr) = 1/9 21

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Assigning probabilities to events 2. Probability that two of the same color are drawn 3. P( A and B) 4. P(A or B) 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 Second Draw First Draw red green yellow red green yellow P (B) = P(rr) + P(gg) +P(yy) = 1/9 +1/9 +1/9 = 1/3 P(A and B) = P(rr) = 1/9 22
Assigning probabilities to events 2. Probability that two of the same color are drawn 3. P( A and B) 4. P(A or B) 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 Second Draw First Draw red green yellow red green yellow P (B) = P(rr) + P(gg) +P(yy) = 1/9 +1/9 +1/9 = 1/3 P(A and B) = P(rr) = 1/9 P(A or B) = P(rr) + P(gg) + P(yy) + P(rg)+P(gr)+P(ry)+P(yr ) = 7/9 23

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Probability of a compound event Recall that an event is a set of outcomes of interest One or more heads in a two-coin toss At least one red marble in two draws Sometimes, an event is described as a
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