IMO Practice Test — Probability
6 Questions • 15 min • Olympiad level
15:00
Question 1 of 6
medium
Three coins are tossed simultaneously. The probability of getting exactly two heads is:
1/8
3/8
1/2
5/8
Explanation: Sample space: 8 outcomes. Exactly 2 heads: HHT,HTH,THH → 3 favorable → 3/8
Question 2 of 6
medium
A letter is chosen at random from the word "MATHEMATICS". The probability that it is a vowel is:
4/11
5/11
3/11
6/11
Explanation: Vowels: A,A,E,I → 4 vowels, total 11 letters → 4/11
Question 3 of 6
medium
Two dice are rolled. The probability that the sum of the numbers is 7 is:
1/6
1/9
5/36
1/12
Explanation: Favorable pairs: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6 out of 36 = 1/6
Question 4 of 6
medium
A card is drawn from a deck. Find the probability that it is either a spade or a face card.
11/26
25/52
3/13
4/13
Explanation: Spades:13, Face cards:12, Overlap (spade face cards):3 → total=13+12-3=22 → 22/52=11/26
Question 5 of 6
medium
A number is chosen from 1 to 100. Find P(number is a perfect square).
1/10
1/5
3/20
1/4
Explanation: Perfect squares: 1,4,9,16,25,36,49,64,81,100 → 10 numbers → 10/100=1/10
Question 6 of 6
medium
In a single throw of two dice, what is the probability of getting a total of 10?
1/9
1/12
5/36
1/6
Explanation: Favorable: (4,6),(5,5),(6,4) → 3 out of 36 = 3/36 = 1/12