Question

# . Female students at a certain university participate in sports with the following probabilities: Soccer =...

. Female students at a certain university participate in sports with the following probabilities:

Soccer = 0.30 Basketball = 0.20

Tennis = 0.20

Both Soccer and Basketball = 0.10 Both Soccer and Tennis = 0.12 Both Basketball and Tennis = 0.08

All three Sports = 0.06
a. Construct the associated Venn diagram with ALL probabilities specified.

You select one female student at random for an interview, determine the probability she plays

b. at least one of the three sports.
c. exactly one of the three sports.
d. exactly two of the three sports.
e. tennis given she does not play soccer.
f. tennis given she plays exactly one sport. g. exactly one sport given she plays tennis.

#### Homework Answers

Answer #1

let A,B and C are event of playing Soccer , Basketball and Tennis \

 P(A)= 0.3 P(B)= 0.2 P(C)= 0.2 P(AnB)=P(A)+P(B)-P(A U B)= 0.1 P(BnC)=P(B)+P(C )-P(B U C)= 0.08 P(AnC)=P(A)+P(C)-P(A U C)= 0.12
 P(AnBnC)=P(A)+P(B)+P(C)-P(AnB)-P(AnC)-P(BnC)+P(AuBuC)= 0.06

a)

b)

 least one=P(AUBUC)=P(A)+P(B)+P(C )-P(AnB)-P(BnC)-P(AnC)+P(AnBnC)= 0.46

c)

 exactly one =P(A)+P(B)+P(C )-2(P(AnB)+P(BnC)+P(AnC))+3*P(AnBnC) = 0.28

d)

 exactly two = P(AnB)+P(AnC)+P(BnC)-3P(AnBnC)=0.12

e)

P(C|Ac) =P(Ac n C)/P(Ac) =(0.2-0.12)/(1-0.3)=0.1143

f)

P(C|exactly one) =0.06/0.28 =0.2143

g)

P(exactly one |tennis) =0.06/0.2 =0.3

Know the answer?
Your Answer:

#### Post as a guest

Your Name:

What's your source?

#### Earn Coins

Coins can be redeemed for fabulous gifts.

##### Not the answer you're looking for?
Ask your own homework help question
ADVERTISEMENT
##### Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

ADVERTISEMENT