Question

The number of head trauma injuries at a small hospital has a Poisson distribution with a mean of 0.2 per day, with each day independent of every other day. Given that at least one injury has occurred over a (seven-day) week, what is the probability that at least two injuries occurred?

Answer 1

Probability that at least one injury has occurred over a week

= 1- probability of zero injury in a week

= 1- ( (0.2)⁰ * e^-0.2 )/ 0! )⁷ = 0.7534

Probability that at least two injuries occurred in a week

= 1- probability of zero injury occurred in week - probability that one injury happened over a week

= 0.7534 - ((0.2) * e^-0.2 )/1!)*((0.2)⁰ * e^-0.2)/0!)⁶ *7

= 0.7534 - 0.34523 = 0.40817

Required probability = (0.40817 * 0.7534) / 0.7534 = 0.40817