1. PROBABILITY – KARNAUGH MAPS

2. WHAT IS A KARNAUGH MAP?

3. IN A VENN DIAGRAM: A is everything in the ‘A’ circle B is everything in the ‘B’ circle A ∩ B’ means ‘A but not B’ A ∩ B means ‘A and B’ or ‘overlap/intersection of A and B’ A’ ∩ B means ‘B but not A’ A’ ∩ B’ means ‘not A or B’ or ‘everything outside the A and B circles’

4. IN A KARNAUGH MAP: We can set these probabilities out in table form The rows and columns can be added up, for example, if we look at the first column: Pr(A ∩ B) + Pr(A’ ∩ B) = Pr(B) B Not B (B complement) A Not A (A complement) Pr(B) + Pr(B’) = 1 Pr(A) + Pr(A’) = 1

5. They are useful if we have some values out of the table, because we can use them to fill in the gaps BB’ A0.20.5 A’0.2 1 This box should always add to ONE HOW CAN WE USE KARNAUGH MAPS? 0.4 0.6 0.3 0.5

6. HOW CAN WE USE KARNAUGH MAPS? From this, we can answer questions: What is Pr(A ∩ B’)? Pr(A ∩ B’) = 0.3 Refer back to the template to find the different probabilities BB’ A0.20.30.5 A’0.20.30.5 0.40.6 1

7. WORDED PROBLEM USING KARNAUGH MAPS You go to a restaurant where they sell different types of burgers. The probability of choosing a burger at random and getting one with cheese is 0.67, getting a burger with chicken is 0.24, and not getting cheese or chicken is 0.23 Find the probability that the randomly chosen burger: a) Has cheese and chicken b) Has cheese or chicken c) Has no cheese d) Has chicken but no cheese

8. FILLING IN THE KARNAUGH MAP TABLE You go to a restaurant where they sell different types of burgers. The probability of choosing a burger at random and getting one with cheese is 0.67, getting a burger with chicken is 0.24, and not getting cheese or chicken is 0.23 CheeseNot cheese Chicken Not chicken 1 0.67 0.24 0.23 0.33 0.76 0.1 0.53 0.14

9. Find the probability that the randomly chosen burger: a) Has cheese AND chicken Pr(cheese ∩ chicken) = 0.14 b) Has cheese OR chicken Pr (cheese U chicken) = Pr(cheese) + Pr(chicken) – Pr(cheese ∩ chicken) = 0.67 + 0.24 – 0.14 = 0.77 c) Has no cheese Pr(cheese’) = 0.33 d) Has chicken but no cheese Pr(chicken ∩ cheese’) = 0.1 Remember the addition law of probability: Pr(A U B) = Pr(A) + Pr(B) – Pr(A ∩ B) You will need this formula to help figure out unknown values in some Karnaugh maps

10. QUESTIONS TO DO Complete the Karnaugh maps worksheet