IMO Practice Test — Probability (Intro)
6 Questions • 25 min • Olympiad level
25:00
Question 1 of 6
hard
A bag has red, blue, and green marbles. P(red)=0.3, P(blue)=0.5. Find P(green).
0.2
0.3
0.5
0.8
Explanation: All probabilities sum to 1. P(green) = 1 - 0.3 - 0.5 = 0.2
Question 2 of 6
hard
Two dice are rolled. Find P(sum = 7).
1/12
1/9
1/6
1/4
Explanation: Outcomes summing to 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) — 6 outcomes. Total = 36. P = 6/36 = 1/6.
Question 3 of 6
hard
A spinner with 4 equal sections (Red, Blue, Green, Yellow) is spun 80 times. Results: Red=22, Blue=18, Green=25, Yellow=15. Which color had the largest difference from theoretical probability?
Red
Blue
Green or Yellow (tied)
Blue or Yellow
Explanation: Theoretical each = 20. Differences: Red=+2, Blue=-2, Green=+5, Yellow=-5. Green and Yellow both differ by 5.
Question 4 of 6
hard
A bag has 5 red, 3 green, 2 blue marbles. Two marbles are drawn WITHOUT replacement. Find P(both red).
1/6
2/9
5/18
1/4
Explanation: P(first red)=5/10=1/2. P(second red | first red)=4/9. P(both)=1/2 x 4/9=4/18=2/9.
Question 5 of 6
hard
In a raffle, 200 tickets are sold. You buy 5 tickets. What is P(win)?
0.025
0.05
0.075
0.10
Explanation: P(win) = 5/200 = 0.025
Question 6 of 6
hard
An experiment has 3 possible outcomes: A, B, C. P(A) = 0.4 and P(B) = 0.35. Find P(C).
0.20
0.25
0.30
0.35
Explanation: P(A)+P(B)+P(C)=1. P(C) = 1 - 0.4 - 0.35 = 0.25