8) a Total of 48 Percent of the Women and 37 Percent of the Men That Took a Certain Quit

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 Starsadvance to the final series, and they have a probability of 0.55 to win eachgame, 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 continuesuntil 7 games are played, even if the Cup winner is determined earlier.

Suppose that the series continues until Dallas Stars win 4 games, evenif 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: