Customers of a hardware shop make a payment either in cash or with credit/debit card with probabilities 0.24 and 0.76, respectively. Assume these probabilities apply to all customers independently. 

(a) If 20 customers pay at the hardware shop, what is the probability that exactly 5 customers pay in cash? Let the random variable X denote the number of customers at the hardware shop who pay in cash. Round your answer to four decimal places (e.g. 98.7654). P(X = 5) = |0.2012 the absolute tolerance is +/-0.0001 (b) What is the probability that the second customer to pay cash is the fifth customer to pay at the shop? Round your answer to four decimal places (e.g. 98.7654). 0.1011 the absolute tolerance is +/-0.0001 (c) Assume that customers arrive according to a Poisson process with a mean of 10.5 per hour. What is the probability that there are no cash transactions in a period of 30 minutes?