Probability with Combinations and Permutations — Unit test
Question 13 • Math Models A
A certain dog can catch a properly thrown tennis ball with a probability of 0.95. Unfortunately, this dog has dropped the last six properly thrown tennis balls. The owner explains that the next throw has to be caught by the dog because he never misses this many.
Answer
A
No, the dog is on a losing streak, so he will drop the next ball thrown.
B
Yes, the dog has missed the last six properly thrown tennis balls, so the next one thrown will be caught.
C
No, the probability of the dog catching a properly thrown tennis ball is 0.95 over the long run, so the owner cannot say what will happen on the next throw.
D
Yes, the dog catches 95% of properly thrown tennis balls, so the next one must be caught to compensate for the previous misses.
Explanation
Each properly thrown ball is a new trial with a 0.95 probability of being caught. The six previous misses do not make the next catch certain or change its probability; the dog could still catch or drop the next ball. Thus the owner cannot know the outcome of the next throw, even though the catch rate is 95% over the long run. Choice C correctly describes this uncertainty.
AI-written and checked against the verified answer.