The Number of Elements Of An Event, Enumeration

theory of probability is used in many fields such physics, economics, weather, forecasting and scientific research. The probability theory is relating to the calculation of the probability or the possibility occurrence of an event. And, an event is part of a larger an event that called the sample space. To obtain the correct calculation of the probability of an event, it necessary to know how many it can happen and how many the sample space can occur. Therefore before we talk about probability, we need to know how to count or to enumerate of occur of an event or many elements of an event. The many of elements of the simple events we can easily to count by firstly register or record all elements of the sample space.

Example1:
Suppose two coins are tossed at the same time. Suppose K is an event that appears are 1 image and 1 number. Determine the number of elements of K.

two coin sides
two coin sides

Suppose N denote the appearing is number, and E denote the appearing is image. Then, the sample space of those tossing of two coins are: NN, NE, EN, EE. So, K as an event that come up are one image and one number has elements: AG, GA. The number of elements of K = 2.

Exercise Competency Test 1.
1. In a die throwing, X denote the event when that legible on the top side of die is prime number. The number of elements of X is …
A. 6 B. 5 C. 4 D. 3 E. 2
Answer: D

A prime number is made only by multiplying two different positif integers those are number 1 and the number itself.

Thus member of prime number are {2,3,5}.

2. In a bridge card taking, suppose X denote the event of the taken card is heart (❤). The number of elements of X is ….
A. 52 B. 39 C. 26 D. 13 E. 4
Answer: D
A set of bridge card contains 52 cards. It consists of 4 types those are heart, diamond, spade, club. Each type has as many cards.
Thus heart type has (52:4=13) cards.

3. In a tossing of three coins simultaneously, K denote the event when appear one number, and two image. The number of elements of K is ….
A. 1 B. 2 C. 3 D. 4 E. 8
Answer: C
Suppose N denote the appearing is number, and E denote the appearing is image. So, K as an event that come up are one image and one number has elements: NEE, ENE, EEN. The number of elements of K = 3.

4. In a throwing of two dice simultaneosly, K denote the event when appears the sum of numbers that legible on the top side is equal to 7. The number of elements of K is ….
A. 4 B. 5 C. 6 D. 7 E. 8
Answer: C

sum of dice numbers
sum of dice numbers

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