2) Suppose there is a bag filled with spheres and cubes that are colored either

Question

2) Suppose there is a bag filled with spheres and cubes that are colored either red, green, or blue. The table below shows the frequency of each type of shape Color Red Blue Green Red Blue Green Shape Sphere Sphere Sphere Cube Cube Cube Frequency 12 13 17 One shape is pulled from the bag at random. Define S as the event a Sphere is pulled as the event a Cube is pulled. Define R as the event a Red shape is pulled. Define B as the event a Blue shape is pulled Define G as the event a Green shape is pulled. a. Find P(S) (1 point) b. Find P(Cn B) (1 point) c. Find P(C U B) (1 point) d. Find P(C ) (1 point) e. Find P(S U C) (1 point)

Explanation / Answer

Solution

(a) P(Sphere) = (7+12+5)/(7+12+5+13+6+17) = 24/60=0.4

(b) P(C and B) = P(Cube and blue) = 6/(7+12+5+13+6+17) = 0.1

(c) P(C union B) = P(C)+P(B)-P(C and B) = 36/60+18/60 - 0.1 = 0.6+0.3-0.1 = 0.8

(d) P(C given B) = P(C and B)/P(B) = 0.1/0.3 = 1/3

(e) P(S union C) = P(S)+P(C)-P(S and C) = 24/60 + 36/60 - 0 = 0.4+0.6 = 1

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