2019 ASRJC P2 Q9

In preparation for an upcoming event, a student management team is considering having meetings on this Friday, Saturday and Sunday. The probability that the meeting is conducted on Friday is \(\frac{1}{6}\). On each of the other days, the probability that a meeting is conducted when a meeting has already been conducted on the previous day, is \(\frac{2}{5}\) and the probability that a meeting is conducted, when a meeting has not been conducted on the previous day, is \(\frac{1}{3}\).

Find the probability that

1. a meeting is conducted on Sunday,[3]
2. a meeting is not conducted on Friday given that there is a meeting on Sunday.[3]

The student management team consists of \(7\) girls and \(3\) boys. At one of the meetings, they sit at a round table with \(10\) chairs.

3. Find the probability that the girls are seated together.[2]

Two particular boys are absent from the meeting.

4. Find the probability that two particular girls do not set next to each other.[3]