In this part of the question, you should calculate the required probabilities - show your working. In England, the most serious emergency calls requesting an ambulance are classified as 'Red 1'. According to data from NHS England, in March 2017, the London Ambulance Service (LAS) received a total of 1597 Red 1 emergency calls. Based on this number and adjusting for variations during the day, suppose that Red 1 calls arriving at the LAS in daylight hours may be modelled as a Poisson process with rate 3 per hour. (1) Write down the distribution of the number of Red 1 calls arriving at the LAS in a 30-minute period during daylight hours, including the values of any parameters. (2) Calculate and report the probability that three Red 1 calls arrive at the LAS in 30 minutes during daylight hours.

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