A bank has studied its chequing accounts and found that 90% of all chequing accounts have been open for at least one year, the remaining percentage of chequing accounts have been open for less than a year. The bank also determined that for all chequing accounts that have been open for less than one year, the percentage of cheques returned due to insufficient funds is 5%. For chequing accounts that have been open for at least one year, only 2% of cheques were returned due to insufficient funds.

(a) What is the probability that a cheque processed by this bank will be returned due to insufficient funds? (b) If a cheque is returned due to insufficient funds, what is the probability that it came from a bank account that has been open for less than one year?

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