All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)

(ii)

(iii)

P(B’|A)

(iv)

since A and C are independent

(v)

Cultivating Champions, Moulding Success

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)

(ii)

(iii)

P(B’|A)

(iv)

since A and C are independent

(v)

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)

Let X and Y denote the mass of a apple and pear in grams respectively.

(3 SF)

(ii)

(3 SF)

(iii)

Let A and B denote the mass of a peeled apple and peeled pear in grams respectively.

(3 SF)

(i)

Number of ways ways

(ii)

Number of ways ways

(iii)

Number of ways ways

(iv)

Case 1: 2 A’s together and B’s separated

Case 2: 2 B’s together and A’s separated

Case 3: 2 A’s together and 2 B’s together

720

Number of ways =10080 – 1800 – 1800 – 720 = 5760 ways

(i)

Graph to be inserted

(ii)

(a) (4 DP)

(b) (4 DP)

(c) (4 DP)

(iii)

Using GC,

(3 SF)

(iv)

(3 SF)

(i)

since A and B are independent.

(ii)

(iii)

If ,

(maximum)

If ,

(minimum)

Let X denote the mass of pineapple tarts and denote the population mean mass of pineapple tarts.

Unbiased estimate of population mean = 0.8825

(3 SF)

Under

Test Statistic, at 10% level of significance.

Using GC, p-value

, do not reject

There is insufficient evidence at 10% significance level to reject the stall owner’s claim.

(i)

Firstly, the average number of errors per page is constant.

Secondly, the number of errors in a page is independent of the number of errors in another page.

(ii)

Let X denote the number of errors per page.

(3 SF)

(iii)

Using GC,

Least

(i)

Let X denote the number of red sweets in a small packet of 10 sweets.

(3 SF)

(ii)

Let Y denote the number of red sweets in a large packet of 100 sweets.

Since n is large,

approximately

by continuity correction

(3 SF)

(iii)

Let W denote the number of packets out of 15 packets that contain at least 30 red sweets.

(3 SF)

(i)

Manager is unable to obtain an appropriate sampling frame.

(ii)

Manager can consider taking equal number of respondents from adults and aged first. Then, he can stand outside the supermarket, interview whoever walks in, based on his personal preferences until he obtains the number of respondents he require.

(iii)

As he samples based on his own preferences, there might be selection bias.

(a)

Let P(n) be the statement

When n=1, LHS

RHS

Since LHS = RHS, P(1) is true.

Assume P(k) is true for some k,

Want to show P(k+1) is true,

LHS

= RHS

Since P(1) is true, P(k) is true P(k+1) is true, hence, by Mathematical Induction, P(n) is true for all

(b)

(i)

(ii)

(iii)

Least n = 499