Let E, F and G be three events in S with P(E) = 0.58, P(F) = 0.34, P(G) = 0.33, P(E ∩ F) = 0.2, P(E ∩ G) = 0.22, P(F ∩ G) = 0.12, and P(E ∩ F ∩ G) = 0.07. Find P(EC ∩ F ∩ G), P(E ∩ FC ∩ G), and P(E ∩ F ∩ GC).

Question
Asked Sep 11, 2019
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Let EF and G be three events in S with P(E) = 0.58, P(F) = 0.34, P(G) = 0.33, P(E ∩ F) = 0.2, P(E ∩ G) = 0.22, P(F ∩ G) = 0.12, and P(E ∩ F ∩ G) = 0.07. Find P(EC ∩ F ∩ G), P(E ∩ FC ∩ G), and P(E ∩ F ∩ GC).

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Expert Answer

Step 1

Consider E, F and G be three independent events in sample space, S.

P(E) 0.58
P(F) 0.34
P(G) 0.33
P(EnF) 0.2
P(EnG) 0.22
P(FnG) 0.12
P(EnFnG) 0.07
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P(E) 0.58 P(F) 0.34 P(G) 0.33 P(EnF) 0.2 P(EnG) 0.22 P(FnG) 0.12 P(EnFnG) 0.07

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Step 2

The complements of events E, F and G can be obtained as:

P(E)1-P(E)
1-0.58
0.42
P(F)1-P(F)
1-0.34
0.66
P(G)1-P(G)
1-0.33
0.67
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P(E)1-P(E) 1-0.58 0.42 P(F)1-P(F) 1-0.34 0.66 P(G)1-P(G) 1-0.33 0.67

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Step 3

The required probability c...

P(E FnG) P(E )x P(F)x P(G)
0.42x 0.34 x 0.33
0.047
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P(E FnG) P(E )x P(F)x P(G) 0.42x 0.34 x 0.33 0.047

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