F.5 Easter

{x , x + 2 , x + 4 , x + 8 , x + 6} and {x + 1, x + 5 , x + 3 , x + 9 , x + 7} are two groups of numbers. Which of the following is/are true?
(You may choose more than one answer)

The standard deviation of the four numbers m - 7 , m - 1 , m + 1 and m + 7 is

If A is 30% greater than B and B is 30% less than C, then

In a test, there are two questions. The probability that Mary answers the first question correctly is 0.3 and the probability that Mary answers the second question correctly is 0.4. The probability that she answers at least one question correctly is

A cone of height 30cm is cut by a plane parallel to its base into a smaller cone of height 10cm and a frustum. Find the ratio of the volume of the smaller cone to the volume of the frustum.

Let a, b, c and d be the mean, the median, the mode and the range of the group of number { x , x , x , x , x , x , x + 1, x + 1, x + 2 , x + 3} respectively. Which of the following must be true? (You may choose more than one answer)

If the mean of the ten numbers 8, 6, 6, 6, 7, 4, 10, 9, 9, x is 7, find the median of the ten numbers.

If the mean of the numbers 3, 3, 3, 3, 4, 4, 5, 5, 6, x is also x, which of the following is/are true?

Which of the following statistics could not be obtained directly from the box-and-whisker diagram? (You may choose more than one answer)

Peter has one $1 coin, one $2 coin and one $5 coin in his pocket. If Peter takes out two coins randomly from his pocket, then the probability that he will get enough money to buy a pen of price $3.5 is

In a certain game, the probability that John will win is 0.3. If he plays the game 3 times, find the probability that he will win at least once.

The mean weight of 36 boys and 32 girls is 46 kg. If the mean weight of the boys is 52 kg, then the mean weight of the girls is

In a school, 55% of the students are boys. It is given that 60% of the boys and 30% of the girls live in Kowloon. Find the probability that a randomly selected student form the school is a girl who lives in Kowloon.

In triangle ADE. B and C are two points on AD and AE such that BC // DE. If AC : CE = 3 : 4, the ratio of the area of triangle ABC to that of BCED.

The variance of data {a , b , c , d} is 16 , find the variance of {10a + 1 , 10b + 1, 10c + 1 , 10d + 1}.

5 boys and 3 girls are arranged in a line. Find the number of arrangement if all girls stand next to each other.

In the triangle ABC. D is a point on AB such that AD : DB = 1 : 2. E is a point on AC such that AE : EC = 3 : 2. Find the ratio of the area of triangle BDE to that of triangle ABC.

A rectangular blanket loses 10% of its length and 8% of its width after washing. The percentage loss in area is

ABCD is a rectangle. M is the mid point of BC and the diagonal AC intersect MD at N. Find the ratio of the area of triangle NCD to that of ABMN.

3 balls are randomly selected form 5 red balls and 6 green balls. Find the probability that 2 red balls are selected.

There are two questions in a test. The probability that David answers the first question correctly is 1/2 and the probability that David answers the second question correctly is 1/3. Given that David answers at least one question correctly in the test, find the probability that he answers the second question correctly.

Which of the following CANNOT be read directly from a cumulative frequency curve? (You may choose more than one answer)

In the figure, the pie chart shows the monthly expenditure of a family. If the family spends $4800 monthly on rent, what is the monthly expenditure on entertainment？

The mean of a set of 9 numbers is 12. If the mean of the first 5 numbers is 8, the mean of the other four numbers is

Let f(x) = 2x² + ax – 3, where a is a constant. If f(x) is divisible by 2x + 1, find the remainder when f(x) is divided by x – a.

If a fair die is thrown three times, then the probability that the three numbers thrown are all different is

2 numbers are randomly selected from {1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10}.
Find the probability that both numbers are less than the median.

5 boys and 3 girls are arranged in a line. Find the number of arrangement if all girls are separated.

A bag contains n white balls and 12 red balls. If a ball randomly drawn from the bag, then the probability of drawing a red ball is 0.25. Find the value of n.

2 fair dice are thrown. Find the probability that the sum of the two numbers thrown is not less than 10.

Ten years ago, the mean age of a band of 11 musicians was 30. One of them is now leaving the band at the age of 40. What is the present mean age of the remaining 10 musician?

If 1 Australian dollar is equivalent to 4.69 H.K. dollars and 100 Japanese yen are equivalent to 5.35 H.K. dollars, how many Japanese yen are equivalent to 1 Australian dollar? Give your answer correct to the nearest Japanese yen.

The line segments AB and DC are parallel. The line segments AC and BD intersects at E. it is known that the area of triangle ABE and triangle CDE are 4 and 9 respectively. Find the area of triangle BCE.

The figure shows the cumulative frequency curves of three distributions.
Arrange the three distributions in the order of their standard deviations,
from the smallest to the largest.

Bag X contains 1 white ball and 3 red balls while bag Y contains 3 yellow balls and 6 red balls. A ball is randomly drawn from bag X and put into bag Y. If a ball is now randomly drawn from bag Y, then the probability that the ball drawn is red is

Consider the data set I : {a , b , c , d} and data set II : {2a + 1 , 2b + 1 , 2c + 1 , 2d + 1}. It is known that the standard score of b in data set I is 3. Find the standard score of b in data set II.

A group of n numbers has mean m. If the numbers 1, 2 and 6 are removed from the group, the mean of the remaining n–3 numbers remains unchanged. Find m.

One letter is chosen randomly from each of the two words ‘CUBE’ and ‘CONE’. Find the probability that the two letters chosen are different.

x is the mean of the group of numbers {a, b, c, d, e}. Which of the following statements about the two groups of numbers {a, b, c, d, e} and { a, b, c, d, e, x} must be true? (You may choose more than one answer)

If a : b = 3 : 4 and b : c = 2 : 5, then a² : c² =