A card is drawn from a standard deck. Find the probability of drawing an ace or a king. Using the Complement Rule to Compute Probabilities We have discussed how to calculate the probability that an event will happen. Sometimes, we are Interested in finding the probability that an event will not happen. The complement of an event E, denoted E’,is the set of outcomes in the sample space that are not in E. For example, suppose we are interested in the probability that a horse will lose a race. If event W is the horse winning the race, then the complement of event W is the horse losing the race. To find the probability that the horse loses the race, we need to use the fact that the sum of all probabilities in a probability model must be 1. P ( E ’ ) = 1 − P ( E ) The probability of the horse winning added to the probability of the horse losing must be equal to 1. Therefore, if the probability of the horse winning the race is 1 9 ,the probability of the horse losing the race is simply. 1 − 1 9 = 8 9
A card is drawn from a standard deck. Find the probability of drawing an ace or a king. Using the Complement Rule to Compute Probabilities We have discussed how to calculate the probability that an event will happen. Sometimes, we are Interested in finding the probability that an event will not happen. The complement of an event E, denoted E’,is the set of outcomes in the sample space that are not in E. For example, suppose we are interested in the probability that a horse will lose a race. If event W is the horse winning the race, then the complement of event W is the horse losing the race. To find the probability that the horse loses the race, we need to use the fact that the sum of all probabilities in a probability model must be 1. P ( E ’ ) = 1 − P ( E ) The probability of the horse winning added to the probability of the horse losing must be equal to 1. Therefore, if the probability of the horse winning the race is 1 9 ,the probability of the horse losing the race is simply. 1 − 1 9 = 8 9
A card is drawn from a standard deck. Find the probability of drawing an ace or a king. Using the Complement Rule to Compute Probabilities We have discussed how to calculate the probability that an event will happen. Sometimes, we are Interested in finding the probability that an event will not happen. The complement of an event E, denoted E’,is the set of outcomes in the sample space that are not in E. For example, suppose we are interested in the probability that a horse will lose a race. If event W is the horse winning the race, then the complement of event W is the horse losing the race. To find the probability that the horse loses the race, we need to use the fact that the sum of all probabilities in a probability model must be 1.
P
(
E
’
)
=
1
−
P
(
E
)
The probability of the horse winning added to the probability of the horse losing must be equal to 1. Therefore, if the probability of the horse winning the race is
1
9
,the probability of the horse losing the race is simply.
1
−
1
9
=
8
9
Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.
7. From a point 20 m away on a level ground, the angle of elevation to the bottom of a
the top of the window is 32°. Calculate the
window is 27° and the angle of elevatim
height of the window.
(3 marks)
32
SOUCAHTOA
Rom
Coso-Adj
opponite
1270
H
X
Hyp
Tant=OPP
Adj
20 #
Zom
Adjacent
CoS2E 20 XHX Tanz 20
20
K
-0.0445503261 -1.764201788
0-044550326 60044550320
(1 mark) 3960
8. All odd numbers from 1 to 10 are arranged in descending order to form a number.
(i) Write the number.
35798.
97531
31
(ii) Write the total value of the second digit of the number formed in (a) (i)
FA 7X1000-7000
이
(1 mark)
9. A cylinder has a diameter of 28 cm and the height is 18 cm. Calculate its volume.
2
22 × 14 × 14 × 18
-110880m
3
(3 marks)
10. The figure below shows a right pyramid with AB = 3 cm, BC = 5 cm, and AV
VC = VD = 4 cm. Draw its net.
V
3+
12
7/18
(2/20
2105
SSS
20
Find the exact values of sin(2u), cos(2u), and tan(2u) given
2
COS u
where д < u < π.
2
Establish the identity.
1 + cos u
1 - cos u
1 - cos u
1 + cos u
= 4 cot u csc u
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MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY