In a study to determine whether preferences for self are more or less prevalent than preferences for others, researchers first asked individuals to identify the person who is most valuable and likeable to you, or your favorite other. Of the 1519 individuals surveyed, 42 had chosen themselves as their favorite other. Source: Gebauer JE, et al. Self-Love or Other-Love? Explicit Other-Preference but Implicit Self-Preference. PLoS ONE 7(7): e41789. doi:10.1371/journal.prone.0041789

(a) Suppose we randomly select 1 of the 1519 individuals surveyed. What is the probability that he or she had chosen himself or herself as their favorite other?

(b) If two individuals from this group are randomly selected, what is the probability that both chose themselves as their favorite other?

(c) Compute the probability of randomly selecting two individuals from this group who selected themselves as their favorite other assuming independence.

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Approach Let event E = "themselves favorite other," so P(E) = number of individuals who select themselves as favorite other divided by 1519, the number of individuals in the survey. To answer part (b), let E = "first person selects themselves as favorite other" and E = "second person selects themselves as favorite other." Then compute P(E1 and E2) = P(E) P(E2|E). To answer part (c), use the Multiplication Rule for Independent Events.