How it works
When every outcome is equally likely,
P(event) = (favourable outcomes) ÷ (total outcomes)
A probability is always between 0 (impossible) and 1 (certain). The probability that something does not happen is 1 − P(it happens), which is often the quicker route.
For "A or B", don't double count the overlap: P(A or B) = P(A) + P(B) − P(A and B). When picking a whole number at random from 1 to N, the number of multiples of k is ⌊N ÷ k⌋, and the multiples of both 6 and 8 are the multiples of their least common multiple, 24. Contest answers are usually simplified fractions.
Probability Basics practice problems with solutions
These problems come from Mathyessy's question bank. Try each one before opening the solution.
A spinner is numbered 1 to 8. What is the probability of spinning an even number?
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Answer: 1/2
The even numbers are 2, 4, 6 and 8: 4 of the 8 equally likely outcomes, so 4/8 = 1/2.
A jar has 6 red and 4 blue marbles. Probability of NOT red?
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Answer: 2/5
4 of the 10 marbles are not red, so the probability is 4/10 = 2/5.
A number is picked from 1 to 40. What is the probability it is a multiple of 6 or 8?
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Answer: 1/4
There are 6 multiples of 6 and 5 multiples of 8. Multiples of both are multiples of 24: just 1 (24). So 6 + 5 − 1 = 10 numbers work, and 10/40 = 1/4.
A number is picked from 1 to 50. What is the probability it is a multiple of 6 but NOT a multiple of 4?
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Answer: 2/25
There are 8 multiples of 6 (6 to 48). Those that are also multiples of 4 are multiples of 12: 12, 24, 36, 48. That leaves 4 numbers, so the probability is 4/50 = 2/25.
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Related topics
Related practice sets in the app
All Counting & Probability topics · Contest math practice by topic · MATHCOUNTS practice · AMC 8 practice