Question

1. Sophie wants to adopt a dog from the shelter. She has categorized the dogs by color (brown or not), size (small or not), and type of fur (fluffy or not). Among the 55 dogs in the shelter:

•  21 dogs are small

•  17 dogs are brown

•  22 dogs have fluffy fur

•  8 dogs are fluffy only

•  9 dogs are small and fluffy

 5 dogs are brown and small
 16 dogs have at least two of the characteristics  14 dogs are not small, not fluffy, and not brown  31 dogs are brown or fluffy

1. a) Draw a Venn diagram for this information.

2. b) How many dogs are small, brown, and fluffy?

3. c) What is the probability that a dog is small, brown, and fluffy?

4. d) What is the probability that a dog is fluffy and brown?

5. e) What is the probability that a dog is not brown?

6. f) What is the probability that a dog is small ONLY?

7. g) What is the probability that a dog is not brown and not fluffy?

8. h) Given that a dog is fluffy, what is the probability that it is small?

9. i) Given that a dog is not brown, what is the probability that it is fluffy?

Answer 1

Let S be the dogs that are small. B be the dogs that are brown. F be the dogs that are fluffy. From the information, N(S) 21 N(B) 17 N(F) 22 N(SnF)-9 P(BuF) 31 From the information, -17+22-31 5+9+8-2N(SnBnF)-16 2N (SnBoF)-5+9+8-16

Using the above obtained values, the Venn diagram is obtained as follows B 14 10 The total number of dog's present are, N -55 The number of dogs that are small, brown and fluffy are, The probability that a dog is small, brown and fluffy is, P(SnBoF)- - 0.0545

The probability that a dog is fluffy, and brown is, N(BnF) P(BnF)- - 0.1455 The probability that the dog is not brown is, P(Not B)-P(B') 10+6+8+14 38 0.6909 The probability that a dog is small ONLY is, 10 0.1818 The probability that a dog is not brown and not fluffy is, 10+14 P(Not B and Not F) 24 - 0.4364

The probability that the dog is small, given the it is fluffy is, P(S) P(F) 9/55 22/55 0.4091 The probability that the dog is fluffy, given that it is not brown is, P(B'nF PlFB')- P(B') (6i8)/5s 38/55 14 38 0.3684