Introduction
Probability has been defined as the likelihood or chance of a specific event occurring. In this case an event can be any of the things that we encounter in our daily lives including the economy of a country growing or students passing exams. It might also be something simple such as listening to a weatherman who gives the daily forecasts of the day and night exposing us to the probability concept. There is a likelihood of one hearing about the following day there is a chance that it will rain or remain sunny. According to Sobecki & Bluman (2015), probability is expressed as the number between one and zero which provides a description of the likelihood of an event occurring. If the probability of an event occurring is almost equal to zero, the interpretation would be that there are high chances that it is impossible to occur. Nevertheless, when the probability of an event occurring is equal to one it is inevitable that it will occur. Probability of an event occurring can either be expressed as a fraction, percentage or a decimal. This means a 50% probability can also be expressed as ½ or 0.5. Sobecki & Bluman (2015) states that in the probability theory, there is what is referred to as the sample space which depicts the set of all possible results or outcomes of the particular random trial or experiment. For instance, in an experiment which involves tossing the coin, the sample space in this case would be the set [tail, head]. In this paper, some of the examples of real world situations which help in understanding what is sample space and probability have been provided. Additionally, the relationship between odds and probability has been presented in detail.

Question #1
The probability that a student fails physics is 0.23. The probability that the student fails chemistry and physics is 0.17. Find the probability that the student fails chemistry given that he or she fails physics.

In this case, of conditional probability, let’s denote the students who failed physics as PH with a probability of 0.23. On the other hand, let us denote the student that failed chemistry and physics to be CP with a probability of 0.23. The question aims to find out the probability P, that the student fails chemistry given that he or she fails physics. This can be equated as P (PH) = 0.23 and P (CP) = 0.17.
Based on this background, the probability that the student fails chemistry given that he or she fails physics is
P (C/PH)= P (CnPH)/PH = 0.17/0.23 =0.739
The above calculation shows that the probability of a student failing chemistry given that he or she fails physics is 0.739.

Question #2
You have purchased a used car. Historically, the chance of spending $2000 in repairs for the car is 72% and the chance of spending $3000 is 28%. What is the expected value of the amount you will spend in repairs for the car?
In this question the scenario is that of purchasing a used car and based on history, the chances of spending $2000 in repairs for the car is 72% or 0.72 while the chance of spending $3000 is approximated as 0.28 or 28%. The critical question is what is the expected value of the amount that to be spend in the car repairs.
The 1st calculation should be on the probability of spending $2000 in the repairs which as stated is 72/100 = 0.72.
On the other hand, the probability of spending $3000 in the repairs of the purchased used car is 28/ 100 which is 0.28.
The expected value that will be spent in the repair of the car will be expressed as [2000 multiplied by the probability of spending $2000 and added by 3000 multiplied by the probability of spending $ 3000]. This will be equal to 1140 (2000*0.72) and (3000*0.28) which is equal to 840. The addition of these two values 1140 and 840 gives 1980.
This means that the expected value of the amount to be spent in the car repair will be $ 1980.
Question #3
The odds in favor of Team A beating Team B are 7:5. What is the probability that Team B will win?
This is a question of odds. In the theory of probability, the probability is often expressed using a number which is between one and zero. On the other hand, odds are expressed by a number that starts from one to the infinity. This means that odds are representative of a ratio of an outcome that is desired and they are not a decimal or a percentage. At times, they can be stated as odds against or odds that are in favor. The odds which are in favor makes a description of the likelihood of an event occurring while the odds which are against makes a description of events which might not occur.
The solution of the probability of Team B winning given that the odds of Team A beating Team B are 7:5 will be determined by dividing the odd of Team B beating Team A with the total of these two. In this case therefore it will be 5/12 which is 0.4167. Thus, the probability that Team B will win the match will be 0.42.
Conclusion
In conclusion, understanding how to calculate probability is significant in many scenarios in the real life. From the above scenarios, probability can be calculated in a number of areas and help in making informed decisions for the benefit of all.
In the first case, the question sought to determine the probability that a student fails Chemistry given that he or she fails physics. When this probability is calculated a student or teacher can make an informed decision on whether a student should continue with either of the subjects or drop one. This is because the concepts of Physics and Chemistry are almost similar and if the probability in each term is that the student will not perform exceptionally in one, a wise decision would be to drop it and concentrate on one only. On the question two, the question wanted to determine the expected value of the amount that will be spent in the car repair using the probability of spending either $ 2000 or $ 3000. Through probability, the individual is able to know the amount which is expected of them during a certain period for the repairs. This will help when budgeting to ensure that the right amount has been saved for the purposes of the repair. If this is not done, the purchased car might not be used for a certain period and it might mean loss of revenue. Thus, probability proves to be critical in matters to do with budgeting. Finally, the third question wanted to determine the probability of a team winning from certain odds given.
In general using probability is a common phenomenon in many of the activities that people are engaged in globally. For instance, many gamblers rely on odds and probability to place their bets either in casinos or football matches. In the case of football matches, the outcome is often unknown and people who bet depend on the history of the performances of team playing to determine the probability.
For instance, if Team A playing against Team B has beaten the opponent for the last 10 matches both home and away the odds will favor it and hence the probability of winning the match is high compared to the Team B. On the other hand when playing the cards often people use probability to determine which are the cards which might be lucky. This is the same guiding factor when people are throwing a dice. Importantly to note is that probability comes from the word probable and hence it’s a guess and the reality might be different with it. For instance, if the probability of Team A winning is high compared to Team B it does not mean that when the match is played A is guaranteed to win. The results after the final whistle might be Team B will win maybe because of the circumstances during the particular time when the match was played such as the pitch condition or one of the players from Team A was shown a red card.

References
Sobecki, D., & Bluman, A. (2015). Math in Our World (3 ed.). New York, New York: McGraw-Hill Education.