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## Main Question or Discussion Point

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.