42) A group of freshmen at a local university consider joining the equestrian te

Question

42) A group of freshmen at a local university consider joining the equestrian team. Thirty?five percent of students choose Western riding, 45% choose dressage, and 50% choose jumping. Twenty percent choose both dressage and jumping, while 10%choose Western and dressage. No one chooses Western and jumping. There are no horses suitable for two styles, and each student is assigned to one horse.

A - What is the probability that a student chooses dressage or jumping?

a) 0.95

b) 0.9

c) 0.23

d) 0.75

B - What is the probability that a student chooses neither dressage nor Western riding?

a) 0.05

b) 0.2

c) 0.5

d) 0.3

C - If two students decide to join the team, what is the probability that both are Western and dressage riders, if they independently decide?

a) 0.8

b) 0.1

c) 0.2

d) 0.01

D - If two students decide to join the team, what is the probability that one student joins jumping only and the other student joins the Western team, if they independently decide?

a) 0.0375

b) 0.105

c) 0.175

d) 0.125

E - If two students decide to join the team, what is the probability that one student joins the dressage team and the other student does not?

a) 0.1925

b) 0.1525

c) 0.2475

d) 0.2275

Explanation / Answer

let Western riding =A ; dressage =B and jumping is C

a)

probability that a student chooses dressage or jumping =P(B u C) =P(B)+P(C)-P(B n C)=0.75

b)

probability that a student chooses neither dressage nor Western riding =1-P(A UB)=1-0.70 =0.3

c)

probability that both are Western and dressage riders, if they independently decide =0.1*0.1=0.01

d)

probability that one student joins jumping only and the other student joins the Western team =

=(0.5-0.2)*(0.35)=0.105

e)

probability that one student joins the dressage team and the other student does not =0.45*(1-0.45)=0.2475

P(A)= 0.35 P(B)= 0.45 P(C)= 0.5 P(AnB)= 0.1 P(BnC)= 0.2 P(AnC)= 0 P(AUB)= 0.7 P(BUC)= 0.75 P(AUC)= 0.85 P(AnBnC) = 0

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