Probability and statistics

Probability basics

Probability questions ask how likely an event is. With three rules you can solve most entrance and early course tasks.

The rules

• Laplace: P(E) = favourable outcomes / all outcomes, if every outcome is equally likely.
• Complement: P(not E) = 1 − P(E). 'At least one' is often easiest via the complement.
• Independent events in a row: multiply the probabilities along the path.
• Different paths to the same result: add their probabilities.

Practice questions with solutions

Generated by the same engine as the Kollego course and solvable without a calculator. Pick an answer in your head, then open the solution.

1. 1. A bag has 4 winning tickets out of 8. You draw one at random. What is the probability of winning, as a percentage?

   • a8%
   • b50%
   • c60%
   • d4%
   Show solution

   Answer: 50%

   P(event) = favourable outcomes ÷ total outcomes.

   4 / 8 = 0.5 = 50%.

2. 2. A bag has 14 winning tickets out of 20. You draw one at random. What is the probability of winning, as a percentage?

   • a20%
   • b14%
   • c30%
   • d70%
   Show solution

   Answer: 70%

   P(event) = favourable outcomes ÷ total outcomes.

   14 / 20 = 0.7 = 70%.

3. 3. The probability that a machine fails on a given day is 75%. What is the probability it does NOT fail?

   • a50%
   • b75%
   • c175%
   • d25%
   Show solution

   Answer: 25%

   P(not A) = 1 − P(A).

   100% − 75% = 25%.

4. 4. The probability that a machine fails on a given day is 25%. What is the probability it does NOT fail?

   • a125%
   • b75%
   • c50%
   • d25%
   Show solution

   Answer: 75%

   P(not A) = 1 − P(A).

   100% − 25% = 75%.

5. 5. The probability that a machine fails on a given day is 20%. What is the probability it does NOT fail?

   • a50%
   • b120%
   • c80%
   • d20%
   Show solution

   Answer: 80%

   P(not A) = 1 − P(A).

   100% − 20% = 80%.

6. 6. The probability that a machine fails on a given day is 60%. What is the probability it does NOT fail?

   • a60%
   • b50%
   • c40%
   • d160%
   Show solution

   Answer: 40%

   P(not A) = 1 − P(A).

   100% − 60% = 40%.

Common mistakes

• Adding probabilities that should be multiplied.
• Calculating 'at least one' directly instead of via the complement.
• Using Laplace when outcomes are not equally likely.

Related topics

All maths topics · T-Kurs · M-Kurs · W-Kurs