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This problem trains for: AMC-10, SAT-II, AMC-12.

On an egg farm, statistics show that the probability for any randomly selected egg to be an A-grade egg is 55%. In a basket of 4 randomly selected eggs, approximately what is the probability that at least 2 are A-grade eggs?

Denote with p the probability of selecting an A-grade egg. The probability of selecting a different grade of egg is 1-p, as the two events are complementary.

The probability to select 4 eggs that are not grade A eggs is:

equation

The probabilty to select 3 eggs that are not grade A eggs and one egg that is grade A is:

equation

but this kind of event can happen in four different ways; the grade A egg is the first one, second one, third one or fourth one in the selection.

In total, the probability of selecting less than 2 A-grade eggs is:

equation

The probability that at least 2 are A-grade eggs is complementary to this one:

equation

Substituting the value for p we get:

equation