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On the average, two birds hit the clock tower on university hall per week and are killed. What is the probability at least one bird was killed last week?

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    Please also explain the answer. Thank you – 2017-01-15
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    There are far too many ambiguous things about this question. Maybe it is a campus tradition that every single week without fail the football team fires a cannon with two live birds stuff inside at the clock tower, thus killing them, rendering not just an average of two birds dying each week by striking the clocktower... but that is the **only** possibility, leaving a probability of $100\%$ that at least one bird was killed last week. On the other hand, perhaps half of the time no birds die and the other half four birds die, yielding an answer of $50\%$. – 2017-01-15
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    In order to come up with any specific answer, one must assume some rather drastic things. The safest assumption would be to model this as a [Poisson Distribution](https://en.wikipedia.org/wiki/Poisson_distribution). Whether it is appropriate or not for this specific case is subjective, but if you do so you can find the probability that zero birds were killed and subtract that away from one to get probability at least one bird was killed. – 2017-01-15
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    It would be good to see some engagement on your part. Very vague question, no wonder you're puzzled. What topics have you been studying lately? – 2017-01-15

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One way to answer is to let the number of birds killed per week be $X \sim Pois(\lambda = 2).$ Then use the formula for the Poisson PDF to evaluate $P(X \ge 1) = 1 - P(X = 0) \approx 0.86.$ (But you should do the problem and show about four decimal places.)

I think this is likely the intended approach if you have just been studying Poisson distributions.

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    Thanks a lot! Saved my day. – 2017-01-15