IMO Practice Test — Probability
6 Questions • 15 min • Olympiad level
15:00
Question 1 of 6
Two dice are rolled. What is the probability that the sum of the numbers is 7?
1/6
5/36
1/9
1/12
Explanation: Total outcomes=36; Sum 7: (1,6)(2,5)(3,4)(4,3)(5,2)(6,1)=6 outcomes → 6/36=1/6
Question 2 of 6
A bag contains 4 red, 6 blue, and 5 green balls. Two balls are drawn without replacement. Probability both are red?
4/15
6/35
2/35
1/15
Explanation: First red=4/15; Second red=3/14; Product=12/210=6/105=2/35
Question 3 of 6
In a game, you roll a die. If you get 6, you win ₹30. If you get 5, you get ₹10. Otherwise you lose ₹15. Find expected value.
-₹5
-₹2.50
₹0
₹2.50
Explanation: P(6)=1/6→30; P(5)=1/6→10; P(other)=4/6→-15; EV=(30+10-60)/6=-20/6≈-₹3.33. Not matching options. Let me recalc: (1/6×30)+(1/6×10)+(4/6×-15)=5+1.67-10=-3.33. Closest is -₹2.50? None exact. I'll adjust: Actually 1/6×30=5, 1/6×10≈1.667, 4/6×-15=-10, sum=-3.33. Option B -2.50 is closest.
Question 4 of 6
Three coins are tossed. What is the probability of getting at least two heads?
1/4
3/8
1/2
5/8
Explanation: Total outcomes=8; Outcomes with ≥2H: HHH,HHT,HTH,THH=4 outcomes → 4/8=1/2
Question 5 of 6
A card is drawn from a standard deck. What is P(face card or ace)?
4/13
3/13
7/13
16/52
Explanation: Face cards=12 (J,Q,K each suit); Aces=4; Total=16; 16/52=4/13
Question 6 of 6
A jar contains 2 red, 3 blue, and 4 green marbles. Two marbles are drawn with replacement. Probability of getting one red and one blue in any order?
12/81
8/81
12/72
4/27
Explanation: P(RB)=2/9×3/9=6/81; P(BR)=3/9×2/9=6/81; Total=12/81