Asked Sep 15, 2019

Let P(E) = 0.45, P(F) = 0.4, and P(FE) = 0.25. Draw a Venn diagram and find the conditional probabilities.

(a)    P(E | FC )

(b)    P(F | EC )
Enter the exact rational fraction, or decimal equivalent rounded to 6 decimal places

Expert Answer

Step 1

Here, P(E)=0.45, P(F)=0.4, P(F∩E)=0.25.

Step 2

Venn diagram:

P(E) = 0.2 (=0.45-0.25), P(F) = 0.15 (=0.4-0.25), P(F∩E) = 0.25 and U= 0.4 (1- P(E)- P(F)- P(F∩E)).


Image Transcriptionclose

U-0.4 P(FE)0.25 F E P(E) 0.2 P(F) 0.15

Step 3

Conditional probability of two events:

The conditional probability is the probability of one event given that the other event has already occurred.

Consider two events...


Image Transcriptionclose

P(E | F) - P(ΕF) P(F)


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