Back to: MATHEMATICS JSS 2
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In today’s Mathematics class, We will be discussing Probability. We hope you enjoy the class!
CONTENT:
i. Experimental Probability
ii. Probability as a fraction
EXPERIMENTAL PROBABILITY
When experimental data are used to predict further events, the prediction is called Experimental Probability. The following examples explain it further:
Example 1: A girl writes down the number of males and female children of her mother and father. She also writes down the number of male and female children of her parents’ brothers and sisters. Her results are shown below:
Number of Children  
Male  Female  
Mother and father  2  5 
Mother’s brothers  6  8 
Mother’s sister  4  8 
Father’s brothers  5  8 
Father’s sisters  7  7 
Totals  24  36 
 Find the experimental probability that hen the girl has children of her own; her firstborn will be a girl.
 If the girl eventually has 5 children, how many are likely to be male?
Solution
 In the girl’s family, there are a total of 60 children. 36 of these are female. If the girl’s own children follow the pattern of her family, then the experimental probability that her firstborn will be a girl is
$\frac{36}{60}=\frac{3}{12}=\frac{1}{4}$
2) Following the family pattern of the girl’s children will be female and will be male. Number of male children that the girl is likely to have out of 5 is equal to 2
Evaluation
 A die has its six faces numbered 1 to 6

 Roll the die 50 times
 How many times did you roll a 6?
 What is the experimental probability of obtaining a 6 on the die?

 Write down the numbers of male and female children in your family. Follow the example above; find the experimental probability that your firstborn child will be a boy.
PROBABILITY AS A FRACTION
Probability is a measure of the likelihood of a required outcome happening. It is usually given as a fraction.
Probability = $\frac{events}{Totolpossibleoutcomes}$
If an outcome is certain to happen, its probability is 1. If an outcome is certain not to happen, its probability is 0 (zero). If the probability of an event happening is P, the probability of the event not happening is 1p.
Example1: it is known that out of every 1000 new cars, 50 develop a mechanical fault in the first 3 months. What is the probability of buying a car that will develop a mechanical fault within 3 months?
Solution
Number of cars developing faults = 50
Number of cars altogether = 1000
Probability of buying a faulty car = $\frac{Numberofcarsdevelopingfaults}{Numberofcarsaltogether}=\frac{50}{1000}=\frac{5}{100}=\frac{1}{20}$
Example2: A market trader has 100 oranges for sale. Four of them are bad. What is the probability that an orange chosen at random is good? ‘At random’ means ‘without carefully chosen’.
Solution
Either:
Four out of 100 oranges are bad, thus 96 out of 100 oranges are good.
Probability of getting a good orange = $\frac{Numberofgoodoranges}{Totalnumberoforanges}=\frac{96}{100}=\frac{24}{25}$
Or:
Probability of getting a bad orange = $\frac{NumberofBadoranges}{Totalnumberoforanges}=\frac{4}{100}=\frac{1}{25}$
Thus,
Probability of getting a good orange = 1 – Probability of getting a bad orange
= $1\u2013\frac{1}{25}=\frac{25}{25}\u2013\frac{1}{25}=\frac{24}{25}$
Example3: City school enters candidates for the WASSCE. The results for the years 1996 to 2000 are given below:
Year  1996  1997  1998  1999  2000 
Number of candidates  86  93  102  117  116 
Number Getting WASSCE Passes  51  56  57  65  70 
 Find the school’s success rate as a percentage.
 What is the approximate probability of a student at City School getting a WASSCE pass?
Solution
1) Total number of passes = 51 + 56 + 57 + 65 + 70 = 299
Total number of candidates = 86 + 93 + 102 + 117 + 116 = 514
Success rate as a fraction = $\frac{299}{514}$ = 0.58 to 2 s.f.
Success rate as a percentage = 0.58 x 100% = 58%
The probability of a student getting a WASSCE pass = 0.58.
EVALUATION
 a) The probability of passing an exam is 0.8. What is the probability of falling the examination?
 b) The probability that a girl win a race 0.6. What is the probability that she loses?
 c) The probability that a pen does not write is 0.05. What is the probability that it writes?
READING ASSIGNMENT
NGMFJSS2. Chapter 121
GENERAL EVALUATION
A bag contains 30 blue pens (B), 10 red pens (R) and 60 white pens (W). If a ball is chosen at random, what is the probability of choosing
(a) a blue pen? (b) a red pen? (c) a white pen? (d)a black pen?
REVISION QUESTION
 In a class of 36 students, 20 are boys. What is the probability of choosing at random a girl as the prefect of the class?
 A ludo die is thrown once. Find the probability of obtaining a PRIME number.
READING ASSIGNMENT
Essential Mathematics Bk. 2 pages 257 – 260
Exercise 20.2 No 1a – f page 259
WEEKEND ASSIGNMENT
 A fair die is thrown 900 times. Find the number of times you would expect to get a 6? A. 200 B. 150 C. 250 D. 100
 The probability that it will be cloudy tomorrow is 0.45. What is the probability that it will not be cloudy tomorrow? A. 0.45 B. 0.35 C. 1.25 D. 0.55
 Find the probability of getting an odd number in a single toss of a fair die?
 A bag contains 5 white, 4 black and 1 blue. One ball is chosen at random. What is the probability that it is black?
 What is the probability that an integer chosen at random between 1 and 10 inclusive is even?
THEORY
 Out of 10 students, the favourite drink of seven is a coke and the favourite drink of the rest is Fanta. One of the students is chosen at random. What is the probability that the favourite drink of the student is


 Coke
 Fanta
 Neither Coke nor Fanta
 Either Coke or Fanta?


 A trader has 100 mangoes for sale. Twenty of them are unripe. Another five of them are bad. If a mango is picked at random, find the probability that it is


 Unripe
 Bad
 Neither unripe nor bad


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In our next class, we will be talking about Pythagoras Theorem. We are very much eager to meet you there.
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