I took some time to realise what is happening.

Basically, the four students are given an option of visiting on a Sat or a Sun.

The only cases where there is NOT at least one student on Sat and at least one student on Sun is when all of them simultaneously visit on the same day.

If all four students make the visit on Sat, then there will be no student visiting on Sun.

Assume that each student is equally likely to choose between a Sat and a Sun.

Probability of this happening
= 1/2 x 1/2 x 1/2 x 1/2
= 1/16

Similarly, if all four students make the visit on Sun, then there will be no student visiting on Sat. The probability of this happening is also 1/16.

In all other cases, there will be at least one student visiting on Sat and one student visiting on Sun.

Since the sum of probabilities of all possible outcomes equal to 1, the probability of having at least one student making a visit on Sat and at least one student making a visit on Sun
= 1 - 1/16 - 1/16
= 14/16
= 7/8

The phrasing should immediately make you of using the complement method :



① P(no student visited on Sunday)
② P(no student visited on Saturday)


So, 1 - these two probabilities.


If you were to do the direct way of calculating :

P(1 Sunday, 3 Saturday)
P(1 Saturday, 3 Sunday)
P(2 Sunday, 2 Saturday)

It would take you much longer and can be confusing.

The phrasing of the question in the last two lines, combined with the fact that original poster mentions that his teachers are also having difficulty with this question, makes my interpretation of the question flawed.

For some reason, I initially thought that each student could choose either Sat or Sun or both. I took it that the question wants the probability that at least one student appears on both the Sat and the Sun sessions. It complicates the story a lot.

Oh. The comment above was actually meant for Redacted.

The phrasing of the question in itself is misleading though.

What is the probability that there is at least one student at both the Saturday’s and Sunday’s events?

It seems to have two different meanings depending on how a person reads it.

Anyway ,

From the first sentence 'Four students can choose to participate in a charity event either on Saturday or Sunday' it should be clear/obvious that it's only 1 of the choices. The word 'both' was not used so we cannot read too much into it.


The second sentence (i.e the question) does require the student to infer so it's actually a reading exercise.

The question has to be consistent in logic with the first sentence so it can only be the case where there on both Saturday and Sunday, there is a minimum of 1 student.

Edit: to add on, whereby each student only attends 1 of those days

If the other meaning was to be implied , then the phrasing would be something along the lines of :

'what is the probability that there is at least one student who attended the event on both days ?'

But for such a question, the option of attending both would have already been stated in the first sentence (which wasn't, so it couldn't have been the other meaning)

I do feel bad for students who are not able to infer these, since the majority of my students do not realise that good command of English is needed just as much as good mathematical skills.

Maybe a little better, though still not the best phrasing, is

What is the probability that in each event, at least one student attends it?

Or

What is the probability that at least one student is present in each of the two events?

“Each” seems to be more appropriate than “both” for the main question.

Even at PSLE , students stumble due to inability to interpret and understand the questions correctly.

At O and A levels, questions like these (especially probability ones with 'and', 'or' and 'either) , one has to be really careful.


LockB once posted a probability question part ​which I misinterpreted as well.


And given the differences in English usage and phrasing/syntax/grammar/vocabulary styles in SG and UK (since the paper is set by Cambridge ), one has to be even more careful at times.

Maybe.

Perhaps the setter tried to differentiate the students' ability by testing their language ability and logical connection.

I remembered last year that some of my students who had seen this question in the o level last year

Express 4^5 as a power of 2

went to put their answer as 32^2

misinterpreting “as a power of 2” as “to the power of 2”.