Question

For a certain soccer team, the time between scoring goals follows an exponential distribution with a mean of 20 minutes. Suppose a game starts at 1:00 p.m. Assume the game is played for 90 minutes without breaks.

(a) What is the probability that the team scores no goals during the Örst 30 minutes?

(b) What is the probability that the team will score its Örst goal between 30 and 60 minutes?

(c) Suppose that no goals are scored before 2:00 p.m.. What is the probability that the teams scores before 2:30 p.m.?

Answer 1

here for exponential distribution parameter β = 20 minutes

a)

  probability that the team scores no goals during the first 30 minutes:

P(X>30)=1-P(X<30)=1-(1-exp(-30/20))=

0.2231

b)

probability that the team will score its first goal between 30 and 60 minutes:

P(30<X<60)=(1-exp(-60/20)-(1-exp(-30/20))=

0.1733

c)

probability that the teams scores before 2:30 p.m given no goal till 2:00

=P( at least one goal in 30 minutes between 2:00 p.m and 2:30 pm)

P(X<30)=1-exp(-30/20)=

0.7769