Lesson 4.5: Probability & Statistics

Probability and Statistics form an important part of the Mathematics section for NDA, CDS, and AFCAT exams. They help aspirants analyze data, calculate chances, and interpret numerical information efficiently.

1. Probability

• Definition: Probability = (Number of favorable outcomes) / (Total number of outcomes)

• Key Formulas:

  • P(E) = n(E)/n(S)

  • Probability of impossible event = 0

  • Probability of certain event = 1

• Example:

  • Probability of getting a head in a coin toss = 1/2

• Applications: Dice, cards, balls in a bag, simple real-life scenarios

2. Statistics

• Mean (Average): Sum of all observations ÷ Number of observations

• Median: Middle value when data is arranged in ascending/descending order

• Mode: Observation occurring most frequently

• Range: Difference between maximum and minimum values

• Example:

  • Observations: 4, 8, 6, 10, 12

    • Mean = (4+8+6+10+12)/5 = 8

    • Median = 8

    • Mode = No mode (all numbers occur once)

    • Range = 12 – 4 = 8

3. Data Interpretation

• Graphs & Charts: Bar graph, Pie chart, Line graph, Tabular data

• Steps to Solve:

  1. Understand the data

  2. Identify what is asked

  3. Apply statistical formulas

  4. Solve systematically

Exam Tips

• Memorize formulas for mean, median, mode, probability.

• Practice data interpretation problems using tables and graphs.

• Solve previous year NDA, CDS, AFCAT probability & statistics questions.

• Focus on accuracy and quick calculation techniques.