Challenging Probability problem 6

The owner of a restaurant counts the number of banquets received by the restaurant at the end of each week. The probability that the restaurant receives at least two banquets in a randomly chosen week is 0.3. A week is considered busy if the restaurant receives at least two wedding banquets in the week.

Calculate the probability that in a period of 6 consecutive weeks, the 6^th week is the second busy week, given that there is at most one busy week in the first four weeks.

Ans: 0.166

Solution