Question

Colleen has 6 eggs, one of which is hard-boiled while the rest are raw. Colleen can't remember which of the eggs are raw. Which of the following statements is true? If Colleen selected one egg, cracked it open and found out it was raw, the probability of selecting the hard-boiled egg on her second pick is 1/5. The probability of Colleen selecting the hard-boiled egg on her first try is 1/5. If Colleen selected one egg, cracked it open and found out it was raw, the probability of selecting the hard-boiled egg on her second pick is 1/6. The probability of Colleen selecting a raw egg on her first try is 1/6.

Answer 1

Answer: If Colleen selected one egg, cracked it open and found out it was raw, the probability of selecting the hard-boiled egg on her second pick is 1/5, and the probability of Colleen selecting the hard-boiled egg on her first try is 1/6.

To see why, let's consider the possible scenarios:

Colleen selects the hard-boiled egg on her first try. There is only 1 hard-boiled egg out of the 6, so the probability of this happening is 1/6.

Colleen selects a raw egg on her first try. There are 5 raw eggs out of the 6, so the probability of this happening is 5/6. After she cracks open the raw egg, there will be 4 raw eggs and 1 hard-boiled egg left. So the probability of selecting the hard-boiled egg on her second pick is 1/5.

Therefore, the statement "If Colleen selected one egg, cracked it open and found out it was raw, the probability of selecting the hard-boiled egg on her second pick is 1/5, and the probability of Colleen selecting the hard-boiled egg on her first try is 1/6" is true.

Explanation: