Question 507804
IF PIZZA SHOP HAS AN ORDER FOR PIZZA WITH "THREE TOPPINGS" AND THE COSTUMERS HAVE A CHOICE OF 12 TOPPINGS, 
1> WHAT IS THE PROBABILITY FROM 1000 PIZAA ,EXACTLY TWO ORDERS ARE EXPECTED THE SAME
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# of combinations of 3 toppings: 12C3 = 220
P(2 orders have the same 3 toppings) = 1/220
Now you have a binomial problem with n = 1000 and p = 1/220
P(x = 2) = 100C2(1/220)^2(219/220)^98 = 7.0911x10^-18
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2> WHAT IS THE PROBABILITY FROM 1000 PIZZA ORDERS,
AT LEAST TWO ORDERS ARE THE SAME.
P(2<= x <=1000) = 1-P(0<= x <=1) = 1-0.0585 = 0.9415
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3> Do THESE PROBABILITIES TRULY REFLECTED REAILITY AND WHY?
Ans: YES
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Cheers,
Stan H.