Question

According to Whole Foods, roughly one out of every 200 grocery items is marked incorrectly. Suppose that a customer has 120 items in his cart. Approximate the probability that there will be 2 or more incorrectly marked items in his cart.

Answer 1

Let X be the number of incorrectly marked items out of 200 in the cart.

Then X ~ Binomial (120, 1/200)

The distribution for first few values of X is:

X	P(X=x)
0	0.547986
1	0.330444
2	0.098801
3	0.019529
4	0.00287
5	0.000335

Now we need to find the probability

P(X>=2)

= 1 - P(X=0) - P(X=1)

= 1 - 0.547986285490042 - 0.330443991250277 = 0.121569723259681

Hence the required probability is 12.157%

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