Roger a baseball player who tends to have streaks hit a home

Roger, a baseball player who tends to have streaks, hit a home run during the first

game of this season. The conditional probability that he will hit at least 1 home run in a

game is 0.4 if he hit at least 1 home run in the previous game, but it is only 0.2 if he didn\'t

hit any home runs in the previous game.

a) What is the probability that Roger will hit no home runs during the third game of this

season?

Solution

Given

Roger, a baseball player who tends to have streaks, hit a home run during the first

game of this season. The conditional probability that he will hit at least 1 home run in a

game is 0.4 if he hit at least 1 home run in the previous game, but it is only 0.2 if he didn\'t

hit any home runs in the previous game.

we have to find the probability that Roger will hit no home runs during the third game of this

season

so for it we have to find the probabilty that he hits at least 1 home run in 2nd game

so

P(he hits at least 1 home runs in second game)=P(he will hit at least 1 home run when he hits at least one home run in 1st game ) + P(he will hits at least one home run when he doesnt hit any run in first game)

=0.4 +0.2=0.6

so he doesn\'t hit any home run in second game is =0.4

so

probability that Roger will hit no home runs during the third game of this

season = 1-P(Roger will hit at least 1 home runs during the third game )

            =1-[ P(he hits in third game and he hits in second game) +P(he hits in third game and he does\'nt hits in second game)]

          =1 - [ 0.4*0.6 +0.2*0.4]

        = 1 - [0.24 +0.08]

      =1-0.32 =0.68   answer