Mixed Practice
This final module combines problems from all sub-categories to test your ability to choose and apply the right probability techniques under exam conditions.
Fundamental Principles
Comprehensive Synthesis
Integrating independent formulas, combination counting, and sample space filtering to efficiently solve complex, multi-step word problems.
Essential Formulation Tips
- Carefully read each problem to check if elements are drawn with or without replacement before building your probability fractions.
Shortcut Execution Techniques
- When tracking complex multi-step scenarios, drawing a quick mental tree diagram can help you map out and organize the different calculation paths.
Contextual Inquiries (FAQs)
Q: What is the best way to speed up my probability calculations?
A:
Example Breakdown: Multi-Step Challenge Problem
High-level review question that tests careful tracking and precision under sequential conditions.Step 1: Calculate the probability that the first ball is red: 4 / 10.
Step 2: Update the remaining ball counts: 3 red and 6 blue balls are left (9 total).
Step 3: Calculate the probability that the second ball is blue: 6 / 9.
Step 4: Multiply the sequential steps together: (4/10) × (6/9) = 24 / 90 = 4 / 15.
Comprehensive Challenge Mixed Set 1
10 advanced questions evaluating cards, coins, dice, and combinations to prepare for competitive exams.
Q1. Two dice are rolled simultaneously. Find the probability that the product of the two face numbers is exactly 12.
Q2. A card is drawn from a standard deck of 52 cards. Find the probability that it is a Queen or a King.
Q3. Three fair coins are flipped at the same time. Find the probability of getting exactly one Head.
Q4. A bag contains 5 red and 5 black items. Two items are drawn without replacement. Find the probability that both items are red.
Q5. A card is drawn from a deck of 52 cards. Given that the drawn card is a face card, find the probability that it is a King.
Q6. An option layout group holds 4 engineers and 2 system admins. If a committee of 2 is chosen at random, find the probability that it includes exactly 1 engineer and 1 system admin.
Q7. A target system has a success rate of 80%. If it operates twice independently, find the probability that it fails both times.
Q8. A number is chosen at random from 1 to 20. Find the probability that it is a multiple of 4 or 5.
Q9. The probability that team alpha wins a game is 0.6. If they play two independent games, find the probability that they win at least one game.
Q10. A student flips a coin and rolls a die. Find the probability of getting a Head on the coin AND a 6 on the die.