It is found that accidents occur at a rate of 0.1 per day in plant A and 0.15 in plant B of GRT. (1) What is the probability that two accidents will occur in the next week (five working days) in A and B? (2) Is the probability that four accidents will occur in the next two weeks twice that of (a)? Justify your answer. (3) Give the average number of accidents per month for GRT. Justify your answer. (4) Give the average number of days without accident for GRT. Justify your answer.

When formulating your answers, please recite the theorems used explicitly and give details of all explicitly and give details of all algebraic steps.