Two strong-man competitors, Atlas and Brutus, are smashing large rocks with great blows of a hammer. Their goal is to smash as many rocks as they can with four strikes. They each get one point for each crumbled rock.
An unstruck rock has a 20% chance of crumbling, a rock that has been struck once but didn't crumble has a 40% chance of crumbling on its second strike, a rock struck twice has a 80% chance of crumbling on its third strike, and a rock that survives 3 strikes is guaranteed to crumble on the fourth.
What is the probability that the final score is a tie?
Note: This problem is highly adapted from a regional math competition for students up to grade 9 and calculators were not allowed. The solution was requested to two decimal places.
(In reply to
would like to understand the contest better.... by Steven Lord)
I can see how this is unclear. No they don't take turns on a single rock.
Each person works on their own rock. If they break it they move on to another new one. What counts is the number of successes.
Yes, each person is guaranteed at least one point.
(The original problem involved alien species improving their civilizations' technological progress. One started with an edge and the question was the probability of them ending up ahead)
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Posted by Jer
on 2023-05-08 13:32:39 |
re: would like to understand the contest better....
