{"id":3531,"date":"2023-10-05T11:10:36","date_gmt":"2023-10-05T11:10:36","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=3531"},"modified":"2023-10-05T11:16:19","modified_gmt":"2023-10-05T11:16:19","slug":"week-8-ss2-third-term-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-8-ss2-third-term-mathematics-notes\/","title":{"rendered":"Week 8 – SS2 Third Term Mathematics Notes"},"content":{"rendered":"

WEEK EIGHT
\n<\/strong>TOPIC: PROBABILITY (EVENT AND OUTCOME)
\n<\/strong>CONTENT
\n<\/strong>1.\u00a0\u00a0\u00a0\u00a0Definition of terms
\n2.\u00a0\u00a0\u00a0\u00a0Events and outcome (measuring probability)
\n\u00a0\u00a0\u00a0\u00a0(a)\u00a0\u00a0\u00a0\u00a0Experimental probability
\n\u00a0\u00a0\u00a0\u00a0(b)\u00a0\u00a0\u00a0\u00a0Theoretical probability <\/p>\n

\u00a0
\n\u00a0DEFINITION OF TERMS
\n<\/strong>(i)Event<\/strong>: When an experiment is performed two or more results or outcomes will be expected to happen. Each attempt is called a trial and the outcome of a trial and the outcome of a trial is called an event, usually denoted by E.
\n(ii)Random Experiment<\/strong>: A random experiment is a repetitive process which may result in any one of the possible outcomes of the experiment OR:
\n(iii)Sample space<\/strong>: The sample space of a random experiment is the set containing all the possible outcomes of the experiment OR:
\nSample space is all the possible outcomes of a trail in an experiment usually denoted by S.
\n(iv)The number of the points in a sample space n(s), and in an event, E is n(E).<\/p>\n

\u00a0Examples
\n<\/strong>1.\u00a0\u00a0\u00a0\u00a0When a coin is tossed twice, all the possible outcomes i.e. the sample space
\n\u00a0\u00a0\u00a0\u00a0S = {HH, HT,TH, TT}
\n\u00a0\u00a0\u00a0\u00a0\\ n(s) = 4
\n2.\u00a0\u00a0\u00a0\u00a0If a die is cast once, there are six outcomes.
\n\u00a0\u00a0\u00a0\u00a0\\ the sample space , S = {1, 2, 3, 4, 5, 6}
\n\u00a0\u00a0\u00a0\u00a0\\ n(S) = 6
\n\u00a0\u00a0\u00a0\u00a0Suppose an event E that an even number is thrown,
\n\u00a0\u00a0\u00a0\u00a0then E = {2, 4, 6} and n(E) = 3.
\n3.\u00a0\u00a0\u00a0\u00a0A box contain 16 red, 6 white, and 18 blues balls.
\n\u00a0\u00a0\u00a0\u00a0The sample spaces, S = {16 + 6 + 18) balls
\n\u00a0\u00a0\u00a0\u00a0n (S) = 40
\n4.\u00a0\u00a0\u00a0\u00a0When a die is tossed twice, the outcome of the first toss S1<\/sup> = (1, 2, 3, 4, 5, 6) does not influence the outcome of the second throw. S2<\/sup> = (1, 2, 3, 4, 5, 6). The two outcomes are independent of each other. For instance, the chance of throwing a5 in the first toss is 1<\/sup>\/6<\/sub> does not influence the chance of the throw of 2 in the second toss (i.e. 1<\/sup>\/6<\/sub>); they are Independent Event. <\/p>\n

\u00a0Equally likely events:<\/strong> Two or more events are said to be equally likely to happen if the chance of occurrence of each of the same.e.g. <\/strong>
\n\t\t1.In the throw of a die, there are six equally likely outcomes, S = {1, 2, 3, 4, 5, 6} the change of each occurring is 1 out of 6 c.c. 1<\/sup>\/6<\/sub>.
\n2.From a pack of 52 cards, the chance of picking any of the cards at random is 1<\/sup>\/5<\/sub>2.<\/p>\n

\u00a0PROBABILITY
\n<\/strong>The probability of an event is the chance of its occurrence, that is the likelihood of the event happening with respect to the sample space.
\nProb. Of E = \u00a0\u00a0\u00a0\u00a0 number of elements in E___
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0number of total elements in S
\n\\P(E) = n(E)
\n\t\t\u00a0\u00a0\u00a0\u00a0 n(S)<\/p>\n

\u00a0NOTE<\/strong>: Probability of an event lies between 0 and 1 i.e. O<P(E) <1
\nthen the prob. that it will not occur is 1 \u2013 P(E).
\nEVALUATION
\n<\/strong>1.\u00a0\u00a0\u00a0\u00a0In a class of 27 boys and 12 girls, what is the probability of picking a girl.
\n2.\u00a0\u00a0\u00a0\u00a0A no is chosen at random from 40 to 50, find the probability that it is a prime number.
\n3.\u00a0\u00a0\u00a0\u00a0If all 2-digits numbers 00, 01, 02, \u2026\u2026.99 are equally likely to be chosen, find the probability that a number picked at random has 5 as its first digit.<\/p>\n

\u00a0EXPERIMENTAL AND THEORETICAL PROBABILITY
\n<\/strong>EXPERIMENTAL PROBABILITY
\n<\/strong>Experimental Prob = no of required outcome
\n\t\t\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0no of possible outcome
\nExample
\n<\/strong>A die is rolled 200 times, the outcome obtained are shown below.<\/p>\n

\n\n\n\n\n
No<\/strong><\/td>\n1<\/td>\n2<\/td>\n3<\/td>\n4<\/td>\n5<\/td>\n6<\/td>\n<\/tr>\n
No. of Outcomes <\/strong><\/td>\n25<\/td>\n30<\/td>\n45<\/td>\n28<\/td>\n40<\/td>\n32<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Find the experimental probability of obtaining (a) 6 (b) 2
\n\t\t\t\t<\/strong>\"\"\/\"\"\/\"\"\/(a)\u00a0\u00a0\u00a0\u00a0P(6)\u00a0\u00a0\u00a0\u00a0= n(6) = 32\u00a0\u00a0\u00a0\u00a0= 4\u00a0\u00a0\u00a0\u00a0
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 n(S)200\u00a0\u00a0\u00a0\u00a0 25 = 0.16
\n(b)\u00a0\u00a0\u00a0\u00a0P(2) = n(2)\u00a0\u00a0\u00a0\u00a0 = 30\u00a0\u00a0\u00a0\u00a0= 3\u00a0\u00a0\u00a0\u00a0 = 0.15
\n\"\"\/\"\"\/\"\"\/\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 n(S)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 200\u00a0\u00a0\u00a0\u00a0 20
\nSince experimental probability uses numerical records of past events to predicts the future, its predictions are not absolutely accurate, however the probability of throwing a 2 on a fair 6-sided die is 1<\/sup>\/6<\/sub>, since any one of the 6 faces is equally alike. This is an example of theoretical probability. <\/p>\n

\u00a0THEORETICAL PROBABILITY
\n<\/strong>Theoretical probability is the assumed value assigned to the occurrence of an event based on the assumption that each of the elements in the outcome are equally likely to happen i.e. by considering the physical nature of the given situation. <\/p>\n

\u00a0Examples
\n<\/strong>Tola throws a fair six-sided die, what is the probability that she throws (a) a 9 (b) a 4
\n(c) a no greater than 2 (d) an even no (e) either 1, 2, 3, 4, 5, or 6?<\/p>\n

\u00a0Solution
\n<\/strong>a.\u00a0\u00a0\u00a0\u00a0Since the faces of a six sided die are numbers 1, 2, \u20266, it is impossible to throw a 9.
\n\u00a0\u00a0\u00a0\u00a0\\ P (9) = 0
\nb.\u00a0\u00a0\u00a0\u00a0There is a chance out of 6 chances of throwing 4
\n\u00a0\u00a0\u00a0\u00a0\\ P(4) = 1\/6
\nc.\u00a0\u00a0\u00a0\u00a0S = {1, 2, 3, 4, 5, 6} , n (S) = 6
\n\u00a0\u00a0\u00a0\u00a0no > 2 = {3, 4, 5, 6} , n(<2) = 4
\n\"\"\/\u00a0\u00a0\u00a0\u00a0P (no >2) = n(no>2) = 4\/6 = 2\/3
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0n(s)\u00a0\u00a0\u00a0\u00a0<\/p>\n

\u00a0d.\u00a0\u00a0\u00a0\u00a0There are 3 possible even number S = {1, 2, 3, 4, 5, 6}, n (S) = 6
\n\u00a0\u00a0\u00a0\u00a0even no = {2, 4, 6} n (even) = 3
\n\u00a0\u00a0\u00a0\u00a0P(even) = n (even) = 3\/6 = \u00bd
\n\t\t\t\"\"\/\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 n (S)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n\t\t\te.\u00a0\u00a0\u00a0\u00a0Either 1, 2, 3, 4, 5, 6
\n\u00a0\u00a0\u00a0\u00a0S = {1, 2, 3, 4, 5, 6}\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0n (S) = 6n (r) = 6.<\/p>\n

\u00a0P(r) = n(r)= 6\/6 = 1<\/strong>
\n\t\t\"\"\/ n(S)\u00a0\u00a0\u00a0\u00a0<\/p>\n

\u00a0Example 2
\n<\/strong>A bag contains 3 red, 5 green and 7 white balls, if a ball is selected from the bag, what is the probability that the ball is green?
\nTotal no. of balls, n(S) = 3 + 5 + 7 = 15
\nEvent E = green balls \\n(E) = 5
\n\\P(E) = n(E) = 5 = 1
\n\t\t\u00a0\u00a0\u00a0\u00a0 n(S) 15 3<\/p>\n

\u00a0EVALUATION
\n<\/strong>Use the figure below to answer the following:<\/p>\n

\n\n\n\n\n\n\n
16<\/td>\n2<\/td>\n3<\/td>\n13<\/td>\n<\/tr>\n
5<\/td>\n11<\/td>\n10<\/td>\n8<\/td>\n<\/tr>\n
9<\/td>\n7<\/td>\n6<\/td>\n12<\/td>\n<\/tr>\n
4<\/td>\n14<\/td>\n15<\/td>\n1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

\u00a0(a)\u00a0\u00a0\u00a0\u00a0If a number is picked at random from the figure. What is the probability that it is:-
\n\u00a0\u00a0\u00a0\u00a0(i)\u00a0\u00a0\u00a0\u00a0Odd (ii)\u00a0\u00a0\u00a0\u00a0Prime (iii)\u00a0\u00a0\u00a0\u00a0even (iv)\u00a0\u00a0\u00a0\u00a0less than 10
\n\u00a0\u00a0\u00a0\u00a0(v)\u00a0\u00a0\u00a0\u00a0Exactly divisible by 3 (vi)\u00a0\u00a0\u00a0\u00a0a perfect square (vii)\u00a0\u00a0\u00a0\u00a0a perfect cube?<\/p>\n

\u00a0(b)\u00a0\u00a0\u00a0\u00a0If a row or column is picked at random from the figure. What is the probability that the total of its no is(i)\u00a0\u00a0\u00a0\u00a034 (ii)\u00a0\u00a0\u00a0\u00a035<\/p>\n

\u00a0GENERAL EVALUATION
\n<\/strong>1\u00a0\u00a0\u00a0\u00a0A bag contains black balls, 3 green balls and 4 red balls, A ball is picked form the bag at random, what is the probability that it is
\n\u00a0\u00a0\u00a0\u00a0(a) Black \u00a0\u00a0\u00a0\u00a0(d) yellow\u00a0\u00a0\u00a0\u00a0(c) Green \u00a0\u00a0\u00a0\u00a0(d) not black (d) either black ore red
\n2\u00a0\u00a0\u00a0\u00a0A school contains 357 boys and 323 girls, if a student is chosen at random, what is the probability that a girl is chosen.<\/p>\n

\u00a0READING ASSIGNMENT
\n<\/strong>NGM SSS2, page113-114, exercise11a, numbers 1-12. <\/p>\n

\u00a0WEEKEND ASSIGNMENT
\n<\/strong>OBJECTIVE
\n<\/strong>\"\"\/\"\"\/1\u00a0\u00a0\u00a0\u00a0What is the probability of throwing a number greater than 4 with a single fair die.
\n (a) \u00bd (b) 1\/3 (c)\u00a0\u00a0\u00a0\u00a05\/6 (d) 2\/3
\n2\u00a0\u00a0\u00a0\u00a0A number is chosen at random from the set (11, 12, 13, \u2026.25) what is the probability that the number is odds?(a) 7\/15\u00a0\u00a0\u00a0\u00a0(b) 8\/15 \u00a0\u00a0\u00a0\u00a0(c) 1\/4\u00a0\u00a0\u00a0\u00a0(d) 3\/4
\n3\u00a0\u00a0\u00a0\u00a0A box contains 8 blues 6 yellow and 10 green balls , one all is picked at random from the box, what is the probability that the ball is yellow. (a) 1\/3 (b)\u00bd (c) 3\/4 (d) 5\/12
\n4\u00a0\u00a0\u00a0\u00a0A coin is tossed twice, what is the probability of obtaining at least a head
\n(a) 3\/4\u00a0\u00a0\u00a0\u00a0(b) 1\/3\u00a0\u00a0\u00a0\u00a0(c) 2\/5\u00a0\u00a0\u00a0\u00a0(d) 1\/2
\n5\u00a0\u00a0\u00a0\u00a0A letter is chosen at random from the word PROBABILITY, what is the probability that the letter is a vowel? (a) 3\/11(b) 4\/11 (c) 5\/11 (d) 6\/11<\/p>\n

\u00a0THEORY
\n<\/strong>1\u00a0\u00a0\u00a0\u00a0Two groups of male students X and Y cast their votes in an election of an officer; he results are as shown in the table below:<\/p>\n\n\n\n\n\n\n
\u00a0<\/td>\nIn favour<\/td>\nAgainst<\/td>\n\u00a0<\/td>\n<\/tr>\n
Group X<\/td>\n152<\/td>\n48<\/td>\n200<\/td>\n<\/tr>\n
Group Y<\/td>\n88<\/td>\n62<\/td>\n150<\/td>\n<\/tr>\n
\u00a0<\/td>\n240<\/td>\n110<\/td>\n\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

<\/sub>
\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0a. How many students participate in the election?
\nb. If a student in favour of the officer is selected, what is the probability that he is from group X?
\nc. A student is choosen at random, what is the probability that he is against the officer?
\n2\u00a0\u00a0\u00a0\u00a0A ltter is choose at random from the alphabet. Find the probability that it is (a) M (b) not A or Z (c) Either P, Q, R, or S (d) One of the letters of NIGERIA.<\/p>\n

\t\t\t\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"

WEEK EIGHT TOPIC: PROBABILITY (EVENT AND OUTCOME) CONTENT 1.\u00a0\u00a0\u00a0\u00a0Definition of terms 2.\u00a0\u00a0\u00a0\u00a0Events and outcome (measuring…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,278],"tags":[],"class_list":["post-3531","post","type-post","status-publish","format-standard","hentry","category-posts","category-third-term-ss2-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/3531","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/comments?post=3531"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/3531\/revisions"}],"predecessor-version":[{"id":3532,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/3531\/revisions\/3532"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=3531"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=3531"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=3531"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}