Thursday, 9 January 2014

PROBABILITY CALCULATIONS --- By. Japhet Masatu.

HOW TO CALCULATE PROBABILITY.

INTRODUCTION:-

Probability is the measure of how an event is likely to occur out of the number of possible outcomes. Calculating probabilities allows you to use logic and reason even with some degree of uncertainty. Find out how you can do the math when you calculate probabilities. Part 1 of 4: Calculating the Probability of a Single Random Event.

1
Define your events and outcomes. Probability is the likelihood of one or more events happening divided by the number of possible outcomes. So, let's say you're trying to find the likelihood of rolling a three on a six-sided die. "Rolling a three" is the event, and since we know that a six-sided die can land any one of six numbers, the number of outcomes is six. Here are two more examples to help you get oriented:
- Example 1: What is the likelihood of choosing a day that falls on the weekend when randomly picking a day of the week?
  - "Choosing a day that falls on the weekend" is our event, and the number of outcomes is the total number of days in a week, seven.
- Example 2: A jar contains 4 blue marbles, 5 red marbles and 11 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is red?
  - "Choosing a red marble" is our event, and the number of outcomes is the total number of marbles in the jar, 20.
2
Divide the number of events by the number of possible outcomes. This will give us the probability of a single event occurring. In the case of rolling a three on a die, the number of events is one (there's only one three on each die), and the number of outcomes is six. You can also think of this as 1 ÷ 6, 1/6, .166, or 16.6%. Here's how you find the probability of our remaining examples:
- Example 1: What is the likelihood of choosing a day that falls on the weekend when randomly picking a day of the week?
  - The number of events is two (since two days out of the week are weekends), and the number of outcomes is seven. The probability is 2 ÷ 7 = 2/7 or .285 or 28.5%.
- Example 2: A jar contains 4 blue marbles, 5 red marbles and 11 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is red?
  - The number of events is five (since there are five total marbles), and the number of outcomes is 20. The probability is 5 ÷ 20 = 1/4 or .25 or 25%. Part 2 of 4: Calculating the Probability of Multiple Random Events.

1
Break the problem into parts. Calculating the probability of multiple events is a matter of breaking the problem down into separate probabilities. Here are three examples:
- Example 1: What is the probability of rolling two consecutive fives on a six-sided die?
  - You know that the probability of rolling one five is 1/6, and the probability of rolling another five with the same die is also 1/6.
  - These are independent events, because what you roll the first time does not affect what happens the second time; you can roll a 3, and then roll a 3 again.
- Example 2:Two cards are drawn randomly from a deck of cards. What is the likelihood that both cards are clubs?
  - The likelihood that the first card is a club is 13/52, or 1/4. (There are 13 clubs in every deck of cards.) Now, the likelihood that the second card is a club is 12/51.
  - You are measuring the probability of dependent events. This is because what you do the first time affects the second; if you draw a 3 of clubs and don't put it back, there will be one less fewer club and one less card in the deck (51 instead of 52).
- Example 3: A jar contains 4 blue marbles, 5 red marbles and 11 white marbles. If three marbles are drawn from the jar at random, what is the probability that the first marble is red, the second marble is blue, and the third is white?
  - The probability that the first marble is red is 5/20, or 1/4. The probability of the second marble being blue is 4/19, since we have one fewer marble, but not one fewer blue marble. And the probability that the third marble is white is 11/18, because we've already chosen two marbles. This is another measure of a dependent event.
2
Multiply the probability of each event by one another. This will give you the probability of multiple events occurring one after another. Here's what you can do:
- Example 1:What is the probability of rolling two consecutive fives on a six-sided die? The probability of both independent events is 1/6.
  - This gives us 1/6 x 1/6 = 1/36 or .027 or 2.7%.
- Example 2: Two cards are drawn randomly from a deck of cards. What is the likelihood that both cards are clubs?
  - The probability of the first event happening is 13/52. The probability of the second event happening is 12/51. The probability is 13/52 x 12/51 = 12/204 or 1/17 or 5.8%.
- Example 3: A jar contains 4 blue marbles, 5 red marbles and 11 white marbles. If three marbles are drawn from the jar at random, what is the probability that the first marble is red, the second marble is blue, and the third is white?
  - The probability of the first event is 5/20. The probability of the second event is 4/19. And the probability of the third event is 11/18. The probability is 5/20 x 4/19 x 11/18 = 44/1368 or 3.2%.

EditPart 3 of 4: Converting Odds to Probabilities

1
Determine the odds. For example, a golfer is favorite to win at a 9/4 odds. The odds of an event is the ratio of its probability that it will will occur to the probability that it will not occur.
- In the example of 9:4 ratio, 9 represents the probability that the golfer will win. 4 represents the probability he will not win. Therefore, it is more likely for him to win than to lose.
- Remember that in sports betting and bookmaking, odds are expressed as "odds against," which means that the odds of an event not happening are written first, and the odds of an events not happening come second. Although it can be confusing, it's important to know this. For the purposes of this article, we will not use odds against.
2
Convert the odds to probability. Converting odds is pretty simple. Break the odds into two separate events, plus the number of total outcomes.
- The event that the golfer will win is 9; the event that the golfer will lose is 4. The total outcomes is 9 + 4, or 13.
- Now the calculation is the same as calculating the probability of a single event.
  - 9 ÷ 13 = .692 or 69.2%. The probability of the golfer winning is 9/13.

EditPart 4 of 4: Knowing the Probability Rules

1
Ensure that two events or outcomes must be mutually exclusive. That means they both cannot occur at the same time.
2
Assign a probability that is a non-negative number. If you arrive at a negative number, check your calculations again.
3
The likelihood of all possible events needs to add up to 1 or 100%. If the likelihood of all possible events doesn't add up to 1 or 100%, you've made a mistake because you've left out a possible event.
- The likelihood of rolling a three on a six-sided die is 1/6. But the probability of rolling all five other numbers on a die is also 1/6. 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 6/6 or 1 or 100%.
4
Represent probability of an impossible outcome with a 0. This just means that there is no chance of an event happening.

TIPS:

You can assign any numbers to events, but they have to be proper probabilities, which means following the basic rules that apply to all probabilities.

You can make your own subjective probability that is based on your opinions about the likelihood of an event. Subjective interpretation of probability will be different for each person.