In a large sample of fish caught in one location, 18% had fungal infections, 10% had fungal and tapeworm infections and 13% were infected with tapeworm. a) Using a Venn diagram or otherwise, find the percentage of the fish that: i) have a tapeworm or fungal infection A. 79% B. 90% C. 11% D. 21% E. 23%

ii) only have a tapeworm infection A. 18% B. 8% C. 12% D. 3% E. 87%

iii) if they have a fungal infection also have a tapeworm infection A. 76.9% B. 33.3% C. 63.6% D. 10% E. 55.6%

iv) have neither a fungal nor tapeworm infection A. 79% B. 90% C. 84% D. 77% E. 89%

b) Are having a fungal and tapeworm infection mutually exclusive? A. Yes, because a fish can have a fungal and tapeworm infection. B. Yes, because having a tapeworm infection doesn't affect the likelihood of having a fungal infection. C. No, because a fish can have a fungal and tapeworm infection. D. No, since having a fungal and tapeworm infection are not independent events. E. No, since having a fungal and tapeworm infection are independent events.

c) In a randomly selected group of 7 fish, calculate the probability that i) exactly 3 of them have a fungal and tapeworm infection A. 0.025 B. 0.108 C. 0.002 D. 0.023 E. 0.001

ii) no more than one fish has a fungal and tapeworm infection A. 0.478 B. 0.850 C. 0.469 D. 0.372 E. 0.150