1 may and jonny are playing paintball in opposite Question

1. may and jonny are playing paintball in opposite ...

Question

1. May and Jonny are playing paintball in opposite teams and they try to shoot
each other simultaneously.
The probability that both May and Jonny hit the target in a single shot is 1/8.
The probability that May hits the target but Jonny misses the target is 3/8.
The probability that May misses the target but Jonny hits the target is 1/8.
The probability that both May and Jonny miss the target is 3/8.
The game ends when one of the two players hits the other. If the two players hit each other
on the same time they both lose.
(a) What is the probability that the battle will end on the n-th round (with the n-th shot
of May or Jonny) ?
(b) What is the probability that Mey wins the game ?
(c) What is the probability that Jonny wins the game ?

Exercise 2. The orange bus line arrives to the station every 15 minutes starting from 5pm.
Fred arrives to the station in a time which is distributed uniformly between 5 to 5 : 45pm.
Fred got out from a recitation and missed the 5pm bus. What is the probability that he will
wait less then 5 min at the station ?

Solution

(a) What is the probability that the battle will end on the n-th round (with the n-th shot
of May or Jonny) ?

3/8 + 1/8 = 4/8 =0.5

(b) What is the probability that Mey wins the game ?

3/8

(c) What is the probability that Jonny wins the game ?

1/8

EXERCISE 2

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