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 Frequency Shape Sphere Sphere Sphere Cube Cube Cube 12 13 6 17 One shape is pulled from the bag at random Define S as the event a Sphere is pulled. Define C 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(C n B) (1 point) C. Find P(C U B) (1 point) d. Find P(C | B) (1 point) e. Find P(S U C) (1 point)

Explanation / Answer

total frequency =7+12+5+13+6+17 =60

a) P(S) =(7+12+5)/60 =0.4

b) P(C n B) =P(cube and blue) =6/60 =0.1

c) P(C U B) =P(C)+P(B)-P(C nB) =(13+6+17)/60+(12+6)/60-6/60=0.6+0.3-0.1 =0.8

d)here P(B) =(12+6)/60 =0.3

P(C|B) =P(C and B)/P(B) =0.1/0.3 =0.3333

e) P(S U C) =1 (as S or C contains all of values)

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