Answer to Question #166420 in Statistics and Probability for Lakshi

Question

There are 12 eggs in a pack. 4 are spoiled ones. If 2 of them are randomly selected, calculate the probability that at least one of them is faulty

Answer 1

At least means one or two spoiled eggs in this task. Consider the situation when we chose one spoiled egg. There are 4*8 = 32 variants (4 spoiled eggs for the first place and 8 remaining for the second). For the situation of two spoiled eggs there are (4*3)/2 = 6 variants (4 spoiled variants for the first place, 3 remaining spoiled eggs for the second, then divide by 2 because the order is not important). So the number of cases favorable for the event is 32 + 6 = 38. The number of total outcomes is 12*11/2 = 66 (12 variants for the first place, and 11 remaining variants for the second, and divide by 2 because the order is not important). The probability is 38/66 = 19/33.