8) A total of 48 percent of the women and 37 percent of the men that took a certain quit
smoking class remained non-smmokers for at least one year after completing the
class.These people then attend a success party at the end of the year.If 62 percent of the
original class were male,what percentage of those attending the party were women?
Sol:
Succesful women : 0.48 percent
Succesful men : 0.37 percent
P( men)=0.62
P(women/ succesful) =
(P(women)*P(succesful/women))/((Pwomen)*P(suc./wmn)+P(men)*(P(suc./men))
= ((1-0.62)*0.48)/(0.38*0.48+0.62*0.37)
10) Suppose that we have 3 cards identical in form except that both sides of the first card
are colored red,both sides of the second card are colored black ,and one side of the third
card is colored black and the other side red.The 3 cards are mixed up in a hat,and 1 card
is randomly selected and put down on the ground.If the upper side of the chosen card is
colored red,what is the probability that the other side is colored black?
Sol:
Let RR,BB,RB denote,respectively, the events that the chosen card is all red,al black,or
the red-black card .Letting R be the event that the upturned side of the chosen card is
red,we have that the desired probability is obtained by
P(RB/R) = P(RB,R)/P(R)
= (P(R/RB)*P(RB)) /(P(R/RR)*P(RR)+P(R/RB)*P(RB)+P(R/BB)*P(BB))
= (1/2*1/3)/(1*1/3+1/2*1/3+0*1/3)
= 1/3
SECTION I QUIZ III SOLUTION
Q10) The Stanley Cup winner is determined in the final series between two teams.The
first team to win 4 games wins the Cup. Suppose that Dallas Stars advance to the final
series, and they have a probability of 0.55 to win each game, and the game results are
independent of each other. Find the probability that
(a) Dallas Stars wins the Stanley Cup
b) seven games are required to determine the Cup winner
Without loss of generality, you can assume that the series continues until 7 games are
played, even if the Cup winner is determined earlier.
Suppose that the series continues until Dallas Stars win 4 games, even if the other rival
wins the Cup earlier. Find the probability that
(c) the series consists of less than 10 games
(d) by the end of the series, the other rival wins at least 3 games
Without loss of generality, you can assume that the series continue until 7 games are
played, even if the Cup winner is determined earlier.
SOL:
(a)
(b) P{X = 3 | n=6, p=.55} = 0.3032
c) X is Negative Binomial (n=4, p=.55).
(P{X < 10} = 0.8342
d) P(X > 6) = 1-P(4)-P(5)-P(6) = 0.5585
SECTION I QUIZ IV SOLUTION
Examples to hypergeometric distribution
Answers: