[Independent and dependent events in a Karnaugh map] There is a well-dressed pen

Question

[Independent and dependent events in a Karnaugh map] There is a well-dressed penguin drinking a martini at Boltini. Let A be the event "Penguin is wearing a bowtie," and let B be the event "Penguin knows how to differentiate ex." Suppose P(A) = 2/3, P(B) = 1/5, and the events A and B are independent. Draw a Karnaugh map of the experimental outcomes. Fill in the probabilities P(AB), P(ABC), P(ACB), and P(ACBC). Suppose P(A) = 2/3, P(B) = 1/5, and P(B|A) = 1/10. Draw a Karnaugh map of the experimental outcomes. Fill in the probabilities P(AB), P(ABC), P(ACB), and P(ACBC).

Explanation / Answer

Refer this http://www.cs.uni.edu/~campbell/stat/prob4.html P(A)=2/3=0.67 so P'(A)=1/3=0.33 P(B)=1/5=0.2 so P'(B)=4/5=0.8 P(AB)=P(A)P(B) So Kmap is A A' B 0.33 0.66 0.2 B' 0.53 0.26 0.8 0.67 0.33 The formulas are P(A&B) P(A&B) P(A|B) = ———————— and P(B|A) = ———————— P(B) P(A)

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