Basics of Probability in Statistics

Probability is a measure of the likelihood of the occurrence of an event. Measures of probability range from 0 to 1; zero means an impossible event and 1 means a certain event.

Terminology

1. Trial or experiment: This refers to an action, the result of which is uncertain. For example, throwing a dice, tossing a coin, etc.

2. Event: This refers to a single result of an experiment.

3. Sample space: This is the total number of possible outcomes of an experiment.

4. Sample point: This refers to one of the possible outcomes.

Formula

The probability of an event = Number of favourable outcomes / Total number of possible outcomes

A few common experiments and important points to remember are as follows:

• Tossing a coin
  This can lead to two possible outcomes:

  • Heads

  • Tails
    The probability of getting either heads or tails is the same, and it is equal to 0.5.

• Throwing a die
  This can lead to six outcomes; you can get any value between 1 and 6, both included:

  • The probability of the occurrence of any number on the die is 1/6.

• Picking a card from a deck of cards
  This can lead to 52 outcomes. A deck consists of:

  • 13 cards of hearts,

  • 13 cards of spades,

  • 13 cards of clubs, and

  • 13 cards of diamonds.
     

• Balls of different colours in a bag
   

Steps to find probability:

1: List every possible outcome of the experiment being performed.

2: Count every possible outcome of the experiment.

3: Count all the favourable outcomes.

4: Use the probability formula to determine the probability of the occurrence of an event.

Demonstrations: Basic Probability

1. If you toss two coins simultaneously, what is the probability of you getting heads in both the cases?

Solution: Total number of possible outcomes = 4, i.e., (H,H), (H,T), (T,H), (T,T)

Total number of favourable outcomes = 1, i.e., (H,H)

Thus, P = 1/4.

2. If you throw two dice simultaneously, what is the probability of you getting the same number on both of them?

Solution: Total number of possible outcomes = 6 x 6 = 36

Total number of favourable outcomes = 6, i.e., (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)

Thus, the probability of you getting the same number on both dice = 6/36 = 1/6.

3. What is the probability of you getting an ace from a deck of cards?

Solution: Total number of favourable outcomes = 4 (ace of each type of card)

Total number of possible outcomes = 52

Thus, P = 4/52 = 1/13.