probability....

Question

1) consider the probability statement regarding events A and B below.

P(A or B) =0.3 ;

P(A and B) = 0.2 ; and

P(A|B) = 0.8

what is P(B)

a) 0.1

2) 0.25

3) 0.375

4) 0.667

2) A suburban high school has a population of 1376 students. The number of students who participate in sports is 649. The number of students who participate in music is 433. If the probability that a student participates in either sports or music is 974/1376 . what is the probability that a student participates in both sports and music?

3) a survey about television - viewing preferences was given to randomly selected freshman and senior at fairpoint high school. the results aree shown below.

favorite type of program

sports reality show comedy series

senior : 83 110 67

freshman: 119 103 54

a student response is selected at random from the results. state the exact probability the student response is from a freshman. given the students prefer to watch reality shows on television.

Answer 1

P(B) = 25% = 0.25

A and B overlap. Draw a Venn diagram. The overlap area has probability = P(A&B)= 0.20

P(A or B) = 0.30. 0.30-0.20 = 0.10 probability of A or B but not both.

Let x = probability of B/~A = P(B/~A)

0.20 = 0.80(0.20+x)

0.20 = 0.16 + 0.80x

0.80x = 0.04

x = 0.04/0.80 = 1/20 = 0.05

0.05 + 0.20 = 0.25 P(B/~A) + P(B/A) = P(B)

P(B) = 0.25

P(S)=649/1376

P(M)=433/1376

P(S or M) = 974/1376

P(S&M) = P(S)+P(M)-P(SorM) = 108/1376

P(S&M) = 27/344

P(Freshman/Reality preference) = 103/(103+110) = 103/213)

Answer 2

1) P(A|B) = P(A and B)/P(B); so P(B)= P(A or B)/P(A|B) = 0.3/0.8 = 0.375;

2) P(sport or music) = P(sport) + P(music) - P(sport and music);

P(sport and music) = P(sport) + P(music) - P(sport or music) = 649/1376 + 433/1376 - 974/1376 = 108/1376 = 27/344

3)P(freshman | reality show) = 103/(103 + 110) = 103/213