Question

At a zoo, a sampling of children was asked if the zoo were to get one additional animal, would they prefer a lion or an elephant. The results of the survey follow:

Write each of the following in terms of events (L/E/B/G, respectively; for example if asked what the probability that a selected child prefers a Lion, given that the child is a Boy, you would

respond: P(L|B) = 90 ) 200

What is the probability that:
a. A randomly selected child is a Boy?
b. A randomly selected Girl prefers Elephants?
c. A randomly selected child that prefers Lions is a Boy d. A randomly selected child prefers Elephants?

Answer 1

(a)

the probability that: a randomly selected child is a Boy : P(B)

(b)

the probability that: a randomly selected Girl prefers Elephants : P(E/G)

(c)

the probability that: a randomly selected child that prefers Lions is a Boy : P(B/L)

(d)

the probability that: a randomly selected child prefers Elephants : P(E)

Answer 2

Based on the information given, let's define the following events:

L = Child prefers Lions E = Child prefers Elephants B = Child is a Boy G = Child is a Girl

a. P(B) = 200 / 200 = 1 (Since all the children in the sample are boys)

b. P(E|G) = 0/0 = undefined (There is no information given about the preference of girls, so we cannot determine the probability)

c. P(B|L) = 90 / (90 + 10) = 0.9 (Out of the children who prefer Lions, 90 are boys and 10 are girls)

d. P(E) = (200 - 90) / 200 = 0.55 (Out of the total sample, 200 children, 90 prefer Lions, so the remaining 110 must prefer Elephants)