SOLUTION: Pizza Time has collected data about customer pizza topping preferences. They have calculated that P(pepperoni) = 0.7, P(olives) = 0.6, and P(pepperoni or olives) = 0.8. Determine t

Question 1005150: Pizza Time has collected data about customer pizza topping preferences. They have calculated that P(pepperoni) = 0.7, P(olives) = 0.6, and P(pepperoni or olives) = 0.8. Determine the P(pepperoni and olives). (2 points)

0.5 is the answer but why??

Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Pizza Time has collected data about customer pizza topping preferences. They have calculated that P(pepperoni) = 0.7, P(olives) = 0.6, and P(pepperoni or olives) = 0.8. Determine the P(pepperoni and olives). (2 points)
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0.5 is the answer but why??
Rule:: P(A and B) = P(A)+P(B)-P(A or B)
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Your Problem:
P(pep or oli) = P(pep)+P(oli)-P(pep or oli)
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= 0.7 + 0.6 - 0.8 = 0.13-0.8 = 0.5
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Cheers,
Stan H.
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Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

p = pepperoni
o = olives
P(p) = 0.7 means that 7 out of 10 people like p OR p & o. Similarly, P(o) = 0.6 means that 6 out of 10 people like o OR p & o. P(p OR o) = 0.8 means that 8 out of 10 people like p OR o OR p & o.

If you add 0.7 and 0.6, you get 1.3 which is greater than 1. Therefore, adding these two values have caused us to count something twice, and that thing we have counted twice is P(p & o). Why? Read on.

P(p) = P(p & ~o) + P(p & o)

P(o) = P(o & ~p) + P(p & o)

P(p OR o) = P(p & ~o) + P(o & ~p) + P(p & o)

P(p) + P(o) = P(p & ~o) + P(p & o) + P(o & ~p) + P(p & o)

P(p) + P(o) - P(p OR o) = P(p & o)

0.7 + 0.6 - 0.8 = 0.5

John

My calculator said it, I believe it, that settles it

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