Please answer proba question.

2. The operating lifetime (in hours) of a phone battery can be described using a continuous sample space S = 1R+ (ie the positive real numbers) by considering events of the type Am. = \"Lifetime of battery exceeds (ie is greater than or equal to) m hours\" and by specifying probabilities of events of this type using the formula P(Am) = exp{(a://\\)2} a: > 0 where A is a positive constant value. For the purpose of the question, A = 2000. (a) Compute the probability that the lifetime exceeds 1000 hours. 1 MARK (b) Compute the probability that the lifetime exceeds 1000 hours if it is known that the lifetime exceeds 500 hours. 2 MARKS (c) If ve identical phone batteries were used under identical operating conditions in five different phones, so that any events concerning the battery lifetimes could be considered mutually inde- pendent, compute that probability that one or more of the battery lifetimes did not exceed 500 hours. 2 MARKS