- #1
Karlx
- 75
- 0
Hi everybody.
I am fighting with the following problem:
In a shooting competition, a team is composed by 2 shooters, who must shoot alternately.
They have probabilities p1 and p2 to hit the target, being p1>p2.
In order to be classified, a team must shoot 3 times and hit the target at least 2 consecutive times.
a) Which one of the two shooters must shoot two times?
b) Generalize the question in the case that they must get at least
two consecutive hits with a total of 2k+1 shoots.
These are my answers:
a)
To me the answer is clear.
The probability for a team of being classified is greater if the worst shooter (that who has probability p2 of hitting the target) shoots in the first and the last turns.
b)
Intuitively, I think the answer is the same. It is better that the worst shooter shoot in the first turn.
But how can I prove my guess.
I´d be grateful for any hint.
Thanks.
I am fighting with the following problem:
In a shooting competition, a team is composed by 2 shooters, who must shoot alternately.
They have probabilities p1 and p2 to hit the target, being p1>p2.
In order to be classified, a team must shoot 3 times and hit the target at least 2 consecutive times.
a) Which one of the two shooters must shoot two times?
b) Generalize the question in the case that they must get at least
two consecutive hits with a total of 2k+1 shoots.
These are my answers:
a)
To me the answer is clear.
The probability for a team of being classified is greater if the worst shooter (that who has probability p2 of hitting the target) shoots in the first and the last turns.
b)
Intuitively, I think the answer is the same. It is better that the worst shooter shoot in the first turn.
But how can I prove my guess.
I´d be grateful for any hint.
Thanks.