☰ Contents · Algebra

Events and probability

Lessons 35–36 · 2 lessons · Sh.A. Alimov, A.R. Xalmukhamedov, M.A. Mirzaakhmedov. Algebra: textbook for Grade 9 of general secondary schools. Revised 4th edition. Tashkent: “O‘qituvchi”, 2019
35

Events

Textbook: pp. 186–189
GoalTell impossible, certain and random events apart, and tell compatible, incompatible and equally likely events apart.
New words
certain event · muqarrar hodisaimpossible event · mumkin bo‘lmagan hodisarandom event · tasodifiy hodisaequally likely events · teng imkoniyatli hodisalar
Explanation

Probability theory studies patterns in random events. An event that always happens under the given conditions is certain, one that never happens is impossible, and one that may or may not happen is a random event. Two events that can happen at the same time are compatible, those that cannot are incompatible. If neither event has an advantage over the other, they are equally likely; for example heads and tails of a fair coin. When a cube has one green face and five red faces, the two colours are not equally likely. Before judging an event, the conditions must be stated clearly.

Worked examples
A die is thrown: “7 points” is impossible; “not more than 6 points” is certain; “an even number of points” is random.
“2 points” and “an odd number of points” are incompatible (2 is even). “4 points” and “more than 3 points” can be compatible (4 fits both).
Class activity

“Event cards”: the teacher reads an event and students raise a card: “certain”, “impossible” or “random”; then for pairs they say “compatible” or “incompatible”. Coin and die trials are done under the teacher’s supervision.

Practice
1
What kind of event is it that all students of a class were born on the same day?
2
Can “today is Thursday” and “today is Monday” be compatible?
3
A box holds 5 white and 1 black ball. Are “white” and “black” equally likely?
4
Why are the colours not equally likely when a cube with one green and five red faces is thrown?