As the first day of Chinese New Year draws to a close, terrifying news have been coming in from all corners of the land.
With Judgement Day falling before Chinese New Year for the first time in living memory, a second “Judgement Day” took place today, as an entire nation of post O-Level students stood in line to be ruthlessly massacred by gossipy relatives thirsty for the blood of their O Level results, JC/Poly choices, singlehood status, IQ level, height and weight, amongst other things.
Escaping today’s carnage only because her house-visiting starts on the second day of CNY, a particular Student now dreads the prospects of facing her three aunties tomorrow i.e. a Gossipy Aunty who likes to compare her son’s exam results with hers, a Kaypoh Aunty who likes to ask if she has a boyfriend, and a very mean Evil Aunty who always say that she “has put on weight compared to last year”, even though her weighing machine showed exactly the same reading year after year.
Having just broken up with her two-timing boyfriend and still anxious of where she’ll end up on Friday, she really fears that her festive season will be ruined by people whom she only meets once a year.
As such, she wishes to find out her odds of survival tomorrow …
Analyzing the historical data of her past visits, there’s a % chance of running into Gossipy Aunty A, a 25% chance of running into Kaypoh Aunty B and a % chance of running into Evil Aunty C in a particular house visit.
- The *probabilities of Gossipy Aunty A asking about her O Level results, asking which JC/Poly she’s going, and showing-off her son’s results are , and respectively.
- The *probabilities of Kaypoh Aunty B asking about her O Level results, asking which JC/Poly she’s going, and asking if she has a boyfriend are , and respectively.
- The *probabilities of Evil Aunty C asking about her O Level results, asking which JC/Poly she’s going, and pointing out that she has gained weight are , and respectively.
Given that each aunty only gets the chance to interrogate/scrutinize her once when they meet, and that there’s absolutely no chance of running into more than one aunty during her visit (∵ they hate each other to the core due to some conflict in their past lives), calculate the probability of her
- being asked about her O Level results.
- being asked about her O Level results or the JC/Poly she’s going.
- escaping any questioning/scrutinizing during the visit.
If she has to make a total of three house visits during this Chinese New Year, and that the probabilities are exactly the same as those described above for each visit, find, correct to 3 significant figures, the probability of her
- escaping any questioning/scrutinizing in at least two visits.
- having a happy Chinese New Year (i.e. avoiding any questioning/scrutinizing on all three visits)
At this point, she realized to her dismay that the carefree months following her O Levels have caused her to generously return all her knowledge of EMaths Probability to her Cher, but she still have a vague memory of her sexy maths tutor saying something to the effort of
For this kind of cheong hei long-winded Probabilty question, it’s important that you draw a Probability Tree Diagram to help you see clearly ALL possible outcomes in the scenario.
Can you help our Student find out if she’s going to have a Happy Chinese New Year tomorrow?