25. Probability
Free study material · concepts, shortcuts & solved questions
For equally likely outcomes, P(E)=favourable outcomes/total outcomes. P(not E)=1−P(E). If A and B are mutually exclusive, P(A or B)=P(A)+P(B). For independent events, P(A and B)=P(A)P(B).
Method before formula Define the sample space before counting. “At least one” is often faster through complement: P(at least one)=1−P(none). Do not multiply mutually exclusive alternatives. |
Formula and decision table
Situation | Probability |
Fair die even | 3/6=1/2 |
Two heads in two coin tosses | 1/4 |
Not drawing an ace | 1−P(ace) |
Worked understanding
A reliable solution has five visible moves: identify the data, choose the base or unit, write the rule, substitute carefully, and check the size of the answer. The examples in this chapter are deliberately small so that the method remains visible.
Calculation discipline Before pressing ahead, state the denominator or unit in words. For example: profit on CP, discount on MP, average over number of items, speed in metres per second, and probability over the fixed sample space. |
Solved examples from this chapter
Question focus | Correct move | Answer |
Probability of even number on a die: | Three of six outcomes are even. | C. 1/2 |
P(not E) when P(E)=0.35: | 1−0.35=0.65. | C. 0.65 |
Independent events combine by: | Joint probability is the product. | B. Multiplication |
What an examiner is testing
The options around Probability usually represent a wrong base, a missed conversion, a sign error or a shortcut used outside its condition. Say the base and unit before calculating, estimate the result, and use substitution or a reverse operation as the final check.
Step-by-step answer construction
Example 1: Probability of even number on a die: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 1/2, because Three of six outcomes are even.
Example 2: P(not E) when P(E)=0.35: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 0.65, because 1−0.35=0.65.
Example 3: Independent events combine by: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is Multiplication, because Joint probability is the product.
Chapter practice
1. Probability of even number on a die:
(A) 1/6 (B) 1/3 (C) 1/2 (D) 2/3
Answer: C. 1/2 | Explanation: Three of six outcomes are even.
2. P(not E) when P(E)=0.35:
(A) 0.35 (B) 0.55 (C) 0.65 (D) 1.35
Answer: C. 0.65 | Explanation: 1−0.35=0.65.
3. Independent events combine by:
(A) Addition only (B) Multiplication (C) Subtraction only (D) Division by zero
Answer: B. Multiplication | Explanation: Joint probability is the product.
SSC CGL speed and trap clinic
For Probability, speed comes after classification. Before calculating, say aloud what the number means, what the denominator is, and what unit the answer must carry. Then use the nearest-option check to catch a sign, base or conversion error.
Checkpoint | What to verify | Typical SSC mistake |
Base | Which quantity is the base in Probability? | Using selling price instead of cost price, or part instead of total |
Unit | Are time, distance, area and rate in compatible units? | Mixing hours with minutes or km/h with m/s |
Direction | Should the answer increase, decrease or stay bounded? | Accepting an impossible negative length or probability above 1 |
Estimate | What range should the answer lie in before exact work? | Trusting a long calculation that is far from the options |
Reverse check | Can the answer be substituted back into the condition? | Stopping at an algebraic value without verification |
Mini decision drill
1. Write the first operation you would perform in a Probability question and why.
2. State the most dangerous denominator or unit in this chapter.
3. Give one condition under which a shortcut would be invalid.
4. Create a small numerical example and verify it by a second method.
Revision evidence Do not tick this chapter because you recognised the formula. Tick it only after you solve one direct question, one altered-condition question and one mixed-paper question correctly. |