# Probability

Welcome to Class !!

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

1. Find the experimental probability that hen the girl has children of her own; her firstborn will be a girl.
2. If the girl eventually has 5 children, how many are likely to be male?

Solution

1. 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

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

1. A die has its six faces numbered 1 to 6
1. Roll the die 50 times
2. How many times did you roll a 6?
3. What is the experimental probability of obtaining a 6 on the die?
2. 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 =

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 1-p.

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 =

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 =

Or:

Probability of getting a bad orange =

Thus,

Probability of getting a good orange = 1 – Probability of getting a bad orange

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
1. Find the school’s success rate as a percentage.
2. 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

1. a) The probability of passing an exam is 0.8. What is the probability of falling the examination?
2. b) The probability that a girl win a race 0.6. What is the probability that she loses?
3. c) The probability that a pen does not write is 0.05. What is the probability that it writes?

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

1. 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?
2. A ludo die is thrown once. Find the probability of obtaining a PRIME number.

Essential Mathematics Bk. 2 pages 257 – 260

Exercise 20.2 No 1a – f page 259

WEEKEND ASSIGNMENT

1. 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
2. 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
3. Find the probability of getting an odd number in a single toss of a fair die?
4. A bag contains 5 white, 4 black and 1 blue. One ball is chosen at random. What is the probability that it is black?
5. What is the probability that an integer chosen at random between 1 and 10 inclusive is even?

THEORY

1. 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
1. Coke
2. Fanta
3. Neither Coke nor Fanta
4. Either Coke or Fanta?
2. 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
1. Unripe

We have come to the end of this class. We do hope you enjoyed the class?

Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.

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

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