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A jar contains 8 red marbles numbered 1 to 8 and 12 blue marbles numbered 1 to 12. A marble is drawn at random from the jar. Find the probability of the given event, please show your answers as reduced fractions.(a) The marble is red. P(red)= (b) The marble is odd-numbered. P(odd)= (c) The marble is red or odd-numbered. P(red or odd) = (d) The marble is blue or even-numbered. P(blue or even) =

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From the information given, the jar contains 8 red marbles and 12 blue marble. The marbles are

Red = 1, 2, 3, 4, 5, 6, 7, 8

Blue = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Probability = number of favorable outcomes/number of total outcomes

number of total outcomes = 8 + 12 = 20

a) number of red marbles = 8

the probability that the marble is red, P(red)= 8/20

Dividing the numerator and denominator by 4,

P(red) = 2/5

b)odd-numbered marbles are

Red = 1, 3, 5, 7

Blue = 1, 3, 5, 7, 9, 11

number of odd-numbered marbles = 10

P(odd) = 10/20

Dividing the numerator and denominator by 10,

P(odd) = 1/2

c) The events can occur together. This means that they are not mutually exclusive. Thus,

P(red or odd) = P(red) + P(odd) - P(red and odd)

P(red and odd) = 4/20

P(red or odd) = 2/5 + 1/2 - 4/20

P(red or odd) = 14/20

Dividing the numerator and denominator by 2,

P(red or odd) = 7/10

d) P(blue or even) = P(blue) + P(even) - P(blue and even)

P(blue) = 12/20

P(even) = 1 - P(odd) = 1 - 1/2 = 1/2

P(blue and even) = 6/20

P(blue or even) = 12/20 + 1/2 - 6/20

P(blue or even) = 16/20

Dividing the numerator and denominator by 4,

P(blue or even) = 4/5

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