A recent dog show had a total of 91 clogs entered in either

A recent dog show had a total of 91 clogs entered in either agility or obedience (but not both); 59 of the dogs were purebred, 44 entered obedience, and 20 mixed breed dogs participated in agility. Find the probability a randomly chosen dog is entered in agility. If a randomly selected dog is entered in obedience, what is the probability it is a purebreed dog? Are the events \"Purebreed\" and \"Agility\" independent? Justify your answer.

Solution

91 dogs entered in a contest.

59 were purebred, so 32 were mixed breed

59 = 44 obedience + 15 agility

32 = 20 agility + 12 obedience

Thus,

a) Total dogs in agility = 15 + 20 = 35

P (dog in agility) = 35 / 91

b)

Dogs in obedience = 44 + 12 = 56

Probability he is pure breed = 44 / 56

= 11/14

c)

No, the events of purebred and agility are not independent because their intersection is not zero.

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