2024 ASRJC H1 Q9

Marketing, Human Resource and Finance are three subjects offered at a business college. The number of students studying different combinations of these subjects are shown in the above Venn diagram. Every student studies at least one of these subjects. The number who study all three subjects is \(x\). One of the students is chosen at random.

• \(M\) is the event that the student studies Marketing
• \(H\) is the event that the student studies Human Resource
• \(F\) is the event that the student studies Finance

1. Write down expressions for \(\mathrm{P}(M)\) and \(\mathrm{P}(H)\) in terms of \(x\).[2]
2. Given that \(M\) and \(H\) are independent, find the value of \(x\).[3]

Using this value of \(x\),

3. find \(\mathrm{P}(M \cup F')\).[1]

Three students are chosen at random, without replacement.

4. Find the probability that exactly two of these three students study exactly all three subjects.[2]