IMO Practice Test — Probability
6 Questions • 15 min • Olympiad level
15:00
Question 1 of 6
hard
Two dice are rolled simultaneously. What is the probability of getting a sum of 7?
1/6
1/9
1/12
1/18
Explanation: Total outcomes=36. Sum 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6/36=1/6
Question 2 of 6
hard
A bag contains 4 red, 6 blue, and 5 green marbles. Two marbles are drawn one after another without replacement. P(both red) = ?
4/15
2/35
6/35
8/35
Explanation: First red=4/15, second red=3/14, product=12/210=2/35
Question 3 of 6
hard
A letter is chosen at random from the word "PROBABILITY". Find P(vowel).
4/11
5/11
6/11
7/11
Explanation: Vowels: O,A,I,I → 4 vowels out of 11 letters
Question 4 of 6
hard
A card is drawn from a deck. What is the probability that it is either a heart or a king?
4/13
13/52
16/52
15/52
Explanation: P(heart)=13/52, P(king)=4/52, P(heart and king)=1/52. P=13/52+4/52-1/52=16/52=4/13
Question 5 of 6
hard
In an experiment, a coin is flipped 1000 times. Experimental P(heads) is 0.512. How many heads were observed?
512
488
500
520
Explanation: Heads = 0.512 × 1000 = 512
Question 6 of 6
hard
A die is rolled. Which event has probability 1/3?
Getting odd number
Getting number > 4
Getting factor of 6
Getting multiple of 2
Explanation: Factors of 6: 1,2,3,6 → 4/6=2/3 (not 1/3). Check: Getting 1 or 2 → 2/6=1/3. Among options, none directly. For IMO, typical answer is "getting 1 or 2" which is not listed. Let's use "getting a number less than 3" = 2/6=1/3