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Probability Matters 概率问题—by Peter 校长
2017-05-04

When calculating the probability of a particular event happening it is best to subdivide the question into three distinct sections:


(a) Firstly, decide how the event can happen,

(b) Secondly, consider in order in which the events can happen,

(c) Thirdly, calculate the numerical probability of the event happening.

 

An example will help to make this process clear.


Consider a box containing 3 red discs, 5 blue discs and 2 yellow discs. A student picks one disc at random from the box, he notes the colour and replaces the disc. He then picks another disc at random, again noting its colour.

Let us answer some probability questions based on this situation.          


1. Find the probability of the student picking two red discs?

(a) How can this event happen?

He first picks a red disc followed by picking another red disc.

(b) In which order can these events happen?

There is only one way to make this selection of discs.

(1) He picks a red disc followed by another red disc.

(c) Calculate the numerical probability of the event happening.

The probability is 0.3 x 0.3 = 0.09


2. Find the probability of the student picking one red and one green disc?

(a) How can this event happen?

He picks two discs, one red and one green.

(b) In which order can these events happen?

There two ways to make this selection of discs.

(1) He picks a red disc followed by green disc,

(2) He picks a green disc followed by red disc.

(c) Calculate the numerical probability of the event happening.

The probability is ( 0.3 x 0.5 ) + ( 0.5 x 0.3 ) = 0.3


3. Find the probability that he does not pick any red discs?

(a) How can this event happen?

He picks two discs, and neither of the disc is red.

(b) In which order can these events happen?

There four ways to make this selection of discs.

(1) He picks a green disc followed by another green disc,

(2) He picks a yellow disc followed by another yellow disc,

(3) He picks a green disc followed by a yellow disc,

(4) He picks a yellow disc followed by a green disc.

(c) Calculate the numerical probability of the event happening.

The probability is

( 0.5 x 0.5 ) + ( 0.2 x 0.2 ) + ( 0.5 x 0.2 ) + ( 0.2 x 0.5 ) = 0.49


I hope you can see from these examples that the most important part of answering the question is to consider the number of ways in which the event can happen. This is closely related to the order in which the events can happen. Making the numerical calculation is easy once you have analysed the problem correctly.


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