Question

# Use the negation rule, together with one or more of the other rules of the probability...

Use the negation rule, together with one or more of the other rules of the probability calculus, to determine the probability that the given event does occur. First indicate the probability that the event does not occur. Then indicate the probability that the event does occur by subtracting the first fraction from 1. Reduce all fractions to the lowest whole numbers. Indicate your answers by typing numeric responses in the spaces provided.

Consider a jar containing two blue balls, two green balls, one red ball, and five yellow balls. What is the probability of drawing either a blue ball, a green ball, or a red ball on three draws (without replacement)? First determine the probability that the event does not happen. Then use the negation rule to determine the probability that the event does happen.

What is the probability that the event does not occur (expressed as a fraction)?

What is the probability that the event does occur (expressed as a fraction)?

(a)

Blue balls = 2

Green balls = 2

Red ball = 1

Yellow balls = 5

Total balls = 10

Event is: Blue OR Green OR Red

Event does not happen = Yellow

To find the probability of drawing Yellow ball in all 3 draws:

Draw 1: Yellow

Blue balls = 2

Green balls = 2

Red ball = 1

Yellow balls = 5

Total balls = 10

P(Draw 1: Yellow) = 5/10 = 1/2

Draw 2: Yellow

Blue balls = 2

Green balls = 2

Red ball = 1

Yellow balls = 4

Total balls = 9

P(Draw 2: Yellow) = 4/9

Draw 3: Yellow

Blue balls = 2

Green balls = 2

Red ball = 1

Yellow balls = 3

Total balls = 8

P(Draw 1: Yellow) = 3/8

Thus,

P(Event does not occur) = 1/2 X 4/9 X 3/8 = 1/12

So,

(b)

P(Event does occur) =1 - 1/12 = 11/12

So,

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