18   7 Animal Crossing is a video game in which players visit desert islands. A single animal lives on each desert island. A player visiting an island will always meet the animal that lives there. Each animal is either male or female. Jonny plays a simplified version of Animal Crossing in which there are only four animal species. Data on the number of animals of each species is shown in Figure 5. Species Alligator Anteater Bear Bird Total Gender Male 6 3 10 15 34 Female 3 7 6 6 22 Total 9 10 16 21 56 [Source: https://animalcrossing.fandom.com/wiki/Animal_Crossing_Wiki] Figure 5 Jonny visits a desert island at random. (a) Write down the probability that the animal he meets is a female anteater. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (b) Write down the probability that the animal he meets is a male, given that it is an alligator. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over 19   Question 7 continued Jonny assumes that once he has visited a particular desert island, he will never visit that island again. (c) Under Jonny’s assumption, find the probability that when Jonny visits four islands, he meets two birds and two bears, given that all the animals he meets are either birds or bears. (5) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ In the full version of Animal Crossing there are more than four species of animal. Jonny’s assumption in part (c) is untrue, and it is possible to meet the same animal multiple times. The data for alligators, anteaters, bears and birds in Figure 5 are correct for both versions of the game. (d) Explain why, in the full version of the game, (i) the probability in part (a) would be smaller than the calculated value (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (ii) the probability in part (b) would be unchanged (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (iii) the probability in part (c) would be smaller than the calculated value. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________