There are three ants at 3 different corners of a triangle. They randomly start…
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There are three ants at 3 different corners of a triangle. They randomly start to move towards each other. What is the probability that they will collide ?
- A.
75%
- B.
100%
- C.
50%
- D.
25%
Attempted by 22 students.
Show answer & explanation
Correct answer: A
Answer: 75%
Each ant randomly chooses one of two directions (clockwise or counterclockwise), independently. So there are 2^3 = 8 equally likely direction combinations.
They avoid any collision only when all three choose the same direction (all clockwise or all counterclockwise). That gives 2 favorable no-collision outcomes out of 8, so probability of no collision = 2/8 = 1/4 = 25%.
Therefore the probability of at least one collision = 1 - probability of no collision = 1 - 1/4 = 3/4 = 75%.