Consider an experiment where the ability of snails to hold firmly onto a smooth substrate is studied. We would like to know if the species of snail is independent of the ability. The snail is attached to a smooth rock and we expose it to water and record if it has the ability to resist the current. Suppose that for such an experiment that the probability that the snail belongs to a particular species A and it is resistant is 0.375. The probability that a snail is resistant is 0.45 and suppose that species A represents 60% of the snails under study.
a) What proportion of snails from species A have the ability to resist the current?
b) Given that the snail has resisted the current, compute the probability that it is a snail from species A.
c) Consider the two events "species A" and "resistant"
i. Are the events mutually exclusive?
ii. Are the events independent?