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Rock concert tickets are sold at a ticket counter. Females and males arrive at times of…

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Rock concert tickets are sold at a ticket counter. Females and males arrive at times of independent Poisson processes with rates 30 and 20 customers per hour. (a) What is the probability the first three customers are female? (b) If exactly two customers arrived in the first five minutes, what is the probability both arrived in the first three minutes. (c) Suppose that customers regardless of sex buy one ticket with probability 1/2, two tickets with probability 2/5, and three tickets with probability 1/10. Let Ni be the number of customers that buy i tickets in the first hour. Find the joint distribution of (N1,N2,N3).