SOLUTION: At Patty the Panda's pizza parlor, the possible pizza toppings are pesto, pepperoni, peppers, and pineapple, and the possible desserts are pumpkin pie, powdered-sugar pretzels, and

Algebra ->  Permutations -> SOLUTION: At Patty the Panda's pizza parlor, the possible pizza toppings are pesto, pepperoni, peppers, and pineapple, and the possible desserts are pumpkin pie, powdered-sugar pretzels, and      Log On


   

Question 1196793: At Patty the Panda's pizza parlor, the possible pizza toppings are pesto, pepperoni, peppers, and pineapple, and the possible desserts are pumpkin pie, powdered-sugar pretzels, and papaya popsicles. If Prajwal the porcupine, Petunia the peacock, and Pete the parakeet each randomly choose a subset of the pizza toppings and a dessert, what is the probability that at least two of them choose the exact same pizza or the same dessert (or both)?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
Using TI or similarly an inexpensive calculator like a Casio fx-115 ES plus
probability that at least two of them choose the exact same pizza
n = 3 ,  p = 1/4 (4 choices of toppings)
P(x ≥ 2) = 1  -  P(x ≤ 1) = 1 - binomcdf(3,1/4, 1) = 1 -  .84375 = .1563
0r
Using P+%28x%29=+highlight_green%28nCx%29%28p%5Ex%29%28q%29%5E%28n-x%29+ 
P+%280%29=+highlight_green%281%29%28.25%5E0%29%28.75%29%5E%283%29+ 
P+%281%29=+highlight_green%283%29%28.25%5E1%29%28.75%29%5E%282%29+ 
P(x ≥ 2) = 1 - .42187 - .42187 = .1563
....................................................
probability that at least two of them choose the exact same dessert
n = 3 ,  p = 1/3 (3 choices of desserts)
P(x ≥ 2) = 1  -  P(x ≤ 1) = 1 - binomcdf(3,1/3, 1)

probability that at least two of them choose the exact same topping and dessert
n = 3 ,  p = 1/12 ( 4*3 = 12 choices for both)
P(x ≥ 2) = 1  -  P(x ≤ 1) = 1 - binomcdf(3,1/12, 1)
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