36
Probability of an event
Textbook: pp. 190–193
GoalCalculate the probability of an event by P(A) = m : n and know that 0 ≤ P(A) ≤ 1.
New words
probability · ehtimollikfavourable outcome · qulaylik tug‘diruvchi natijaelementary outcome · elementar natijaP(A) · P(A)
Explanation
Suppose an experiment has n equally likely, pairwise incompatible outcomes and m of them are favourable to event A. Then the probability of A is P(A) = m : n (the classical definition). The idea of probability took shape in the 17th century in the letters of Pascal and Fermat; the letter P comes from the Latin probabilitas. For a certain event m = n, so P = 1; for an impossible event m = 0, so P = 0. For a random event 0 < m < n, so 0 < P(A) < 1. Every probability lies between 0 and 1 and can be neither negative nor greater than 1.
Worked examples
A box has 3 red, 5 blue and 2 green balls. A green ball is drawn: n = 10, m = 2, P = 2/10 = 1/5.
A prime number of points on a die: 2, 3, 5 are favourable, m = 3, n = 6, P = 3/6 = 1/2.
Class activity
“Probability ruler”: draw a ruler from 0 to 1; students place events they invent (certain, impossible, random) at their positions and compute P.
Practice
1
Cards are numbered 1 to 15. What is the probability of drawing a multiple of 5?
1/5
2
What is the probability of a certain event?
1
3
A box has 4 white and 6 black balls. What is the probability of drawing a black one?
3/5
4
Why can a probability not exceed 1?
Because m ≤ n, so m : n ≤ 1.