Probability and statistics is one of the highest-yield chapters for BCS, bank, and IT-officer written and MCQ exams. Almost every recruitment paper carries questions on the probability of dice, coins and cards, on mean/median/mode, and on standard deviation. The good news: the whole chapter runs on a small set of formulas plus careful counting. If you can count favorable and total outcomes correctly and remember about a dozen formulas, you can solve nearly every question in the time allowed.
This lesson builds the topic from first principles — no prior knowledge assumed — and gives you many fully worked, step-by-step examples in exactly the style exams use.
Learning objectives
- Define sample space, event, and compute probability as favorable ÷ total.
- Solve two-dice sum problems using a sum table, and standard coin and card problems.
- Apply the addition rule, recognise mutually exclusive events, and use the complement.
- Compute conditional probability and test whether events are independent.
- Use permutations and combinations to count outcomes in probability problems.
- Calculate expected value.
- Find mean, median and mode for both ungrouped and grouped data, and use the empirical relation.
- Compute range, quartiles, variance and standard deviation, and apply min-max normalization.
- Distinguish arithmetic, geometric and harmonic means and build a frequency distribution.