Probability: Experiments, Sample space and events Experiment → a process or an operation with outcomes Sample space → set of all possible outcomes of an experiment Event → set of outcomes that fulfill a given condition. 1. The c ards show n bel ow a re pu t into a box . A card is pi cked at ra ndom from the box. Deter mine whi ch of the following is a possible outcomes. (a) A letter "C". (b) Aconsonant. (c) A letter "Z" 2. List the samp le space of the followin g expe riment. (a) A two d igits n umbers is for med fro m the digits 1, 3, 5 and 7. (b) Box A conta ins the c ards labe lled with A, B and C. Box B contains the cards labelled with 1 and 2. A card is pi cked a t rando m from ea ch box . 3. T en ca rds labelled with numbers 21 to 30 are pla ced in a box. A card is picked a t rando m from the box . (a) Determine if the following event are possible. (i) Getting a prime number. (ii) Gett ing a perfect square. (iii ) Getti ng a fr ac ti on . (b) List al l the possible outcomes for the following event. (i ) Gettin g a even number. (i i) Ge tt in g a mult ip le of 3. (i ii ) Ge tt in g a number wi th the sum of digits is 3 E E C R E X I S
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1. Five cards labelled with the numbers 1, 2, 3, 4 and 5 are placed in a box. A card is drawn at random, thenumber on the card is recorded and the card is returned to the box. The process is repeated 84 timesand the result is shown as below.
4. There are x red cards, 16 yellow cards and 10 blue cards in a box. If a card is drawn at random, the
probability that a blue card is picked is2
7. Find the value of x.
5.The probability of Ali scoring a goal from penalty kick is
3
4. If Ali is given 120 penalty kicks. Find the
expected number of goals scored by Ali.
6. A fair dice is rolled 540 times. How many times will it likely get the number "5".
7. A bag contains red and white marbles. If a marble is drawn at random, the probability of getting a red
marble is3
8
. When a marble is drawn at random for k times, 125 times of red marbles is obtained.
Find the value of k.
8. Table shows the number of questions on health, entertainment, sport and history in a question bank.
Category Health Entertainment Sport History
Number of Questions 16 20 24 40
(a) If a question is chosen at random, find the probability of choosing a question on Entertainment.(b) If the number of questions in the question bank is increased to 250 question, how many question
3. Diagram shows a prism.(a) Name the angle between the straight line BD and the
plane ADEF.(b) Find the angle between the straight line BD and the
plane ADEF.
4. Diagram shows a prism.(a) Name the angle between the straight line BD and the
plane CDE.(b) Find the angle between the straight line BD and the
plane CDE.
5. Diagram shows a pyramid with the vertex E is verticallyabove the midpoint of the diagonals of the base.(a) Name the angle between the straight line CE and the
base ABCD(b) Find the angle between the straight line CE and the
base ABCD.
Lines and Planes in 3-Dimensions : Angle between Two Planes
1. Diagram shows a cuboid.(a) Name the angle between the plane CDFG and the
base ABCD(b) Find the angle between the plane CDFG and the
2. Diagram shows a cuboid.(a) Name the angle between the plane BDEG and the
plane ABGF.(b) Find the angle between the plane BDEG and the
plane ABGF.
3. Diagram shows a prism.(a) Name the angle between the plane BDE and the
plane ADEF.(b) Find the angle between the plane BDE and the plane
ADEF.
4. Diagram shows a prism.(a) Name the angle between the plane BCEF and the
plane ADEF.
(b) Find the angle between the plane BCEF and theplane ADEF.
5. Diagram shows a pyramid with the vertex E is verticallyabove the midpoint of the diagonals of the base..(a) Name the angle between the plane CDE and the
base ABCD(b) Find the angle between the plane CDE and the base