(c) In how many ways can 5 copies of a book be distributed among 10 people if each person can get any number of books?
Notice that the difference between (b) and (c) is that the book distributed is not identical. So for (c), we are pretty much distributing identical balls to distinct boxes. Whereas for (b) , we are pretty much distributing distinct balls to distinct boxes.
Each card in a deck of cards bear a single number from 1 to 5 such that there are cards bearing the number , where . One card is randomly drawn from the deck. Let be the number on the card drawn.
(i) Find the probability distribution of .
(ii) Show that and find .
Andrew draws one card from the deck, notes the number and replaces it. The deck is shuffled and Beth also draws on card from the deck and notes the number. Andrew’s score is times the number on teh card he draws, while Beth’s score is the square of the number on the card she draws. Find the value of so that the game is a fair one.
I’ll keep this short since we are all busy. One thing about paper 1 we saw, there were many unknowns.
So topics which I think will come out…
Differentiation – I think a min/max problem will come out, possibly with r and h both not given and asked to express r in terms of h. But students should revise a on the properties of curves with differentiation; given a curve equation with an unknown, for instance , find the range of k such that there is stationary points.
Complex Number – Loci will definitely come out. I’m saying they will combine with trigonometry.
Integration – Modulus integration hasn’t really been tested. Else a question on Area/ Volume could be tested, and I’ll say they need students to do some
For statistics, my students should have gotten the h1 stats this year. And if it’s an indicator, then it should not be a struggle.
I expect PnC and probability to be combined. Conditional Probability in a poisson question should be tested too, so do revise it well. For hypothesis testing, students should be careful of their formula and read really carefully about the alternative hypothesis. Also, :9 know that the formulas for poison PDF and binompdf are both given in mf15. Lastly, know when to use CLT.
On a typical weekday morning, customers arrive at the post office independently and at a rate of 3 per 10 minute period.
(i) State, in context, a condition needed for the number of customers who arrived at the post office during a randomly chosen period of 30 minutes to be well modelled by a Poisson distribution.
(ii) Find the probability that no more than 4 customers arrive between 11.00 a.m. and 11.30 a.m.
(iii) The period from 11.00 a.m. to 11.30 a.m. on a Tuesday morning is divided into 6 periods of 5 minutes each. Find the probability that no customers arrive in at most one of these periods.
The post office opens for 3.5 hours each in the morning and afternoon and it is noted that on a typical weekday afternoon, customers arrive at the post office independently and at a rate of 1 per 10 minute period. Arrivals of customers take place independently at random times.
(iv) Show that the probability that the number of customers who arrived in the afternoon is within one standard deviation from the mean is 0.675, correct to 3 decimal places.
(v) Find the probability that more than 38 customers arrived in a morning given that a total of 40 customers arrived in a day.
(vi) Using a suitable approximation, estimate the probability that more than 100 customers arrive at the post office in a day.
All solutions here are SUGGESTED. KS will hold no liability for any errors. Comments are entirely personal opinions.
As these workings and answers are rushed out asap, please pardon me for my mistakes and let me know if there is any typo. Many thanks.
I’ll try my best to attend to the questions as there is H2 Math Paper 2 coming up.
(rejected since ) or
Using GC, required answer (3SF)
When . So is a minimum point.
When . So is a maximum point.
Area of ABEDFCA
When (rejected since )
The store manager has to survey male students and female students in the college. He will do random sampling to obtain the required sample.
Stratified sampling will give a more representative results of the students expenditure on music annually, compared to simple random sampling.
Unbiased estimate of population mean,
Unbiased estimate of population variance,
[Venn diagram to be inserted]
Find the probability that we get same color. then consider the complement.
Let X denote the number of batteries in a pack of 8 that has a life time of less than two years.
Let Y denote the number of packs of batteries, out of 4 packs, that has at least half of the batteries having a lifetime of less than two years.
Let W denote the number of batteries out of 80 that has a life time of less than two years.
Since n is large,
by continuity correction
Let X be the top of speed of cheetahs.
Let be the population mean top speed of cheetahs.
Using GC, is rejected.
For to be not rejected,
(round down to satisfy the inequality)
[Sketch to be inserted]
Using GC, (3SF)
Time taken minutes
Estimate is reliable since is within the given data range and is close to 1.
Using GC, (3SF)
The answers in (ii) is more likely to represent since is close to 1. This shows a strong positive linear correlation between x and y.
Let X, Y denotes the mass of the individual biscuits and its empty boxes respectively.
The mean number of a particular type of weed that grow on the field is a constant.
A particular type of weed growing on the field is independent of another particular type of weed growing on the field.
Let X be the number of dandelion growing per .
You can find the solutions of all ten sets of the June Revision Exercise we did in class.
June Revision Exercise 1
June Revision Exercise 2 June Revision Exercise 3
June Revision Exercise 4
June Revision Exercise 5
June Revision Exercise 6
June Revision Exercise 7 June Revision Exercise 8
June Revision Exercise 9
June Revision Exercise 10