Question

2) Suppose you’re an ornithologist who specializes in American crows (Corvus brachyrhynchos),and you’ve collected data on 100 such birds. Each bird was classified by sex (male or female),and by size (large or small).
The counts follow:
•Male, Large: 38,
•Male, Small: 13,
•Female, Large: 23,
•Female, Small: 26.
Based on these numbers, what is the probability that a randomly chosen crow from this group is large? What is the probability that a crow is large if it is already known to be male? Is the event of being large independent of the event of being male?

Answer 1

The total number of American crows = 38+13+23+26 = 100

We are given the following probabilities:

P(Male and Large) = 0.38

P(Male and Small) = 0.13

P(Female and Large) = 0.23

P(Female and small) = 0.26

a)

P(Large) = P(Male and Large) + P(Female and Large) = 0.38 + 0.23 = 0.61

b)

P(Large/Male)

= P(Large and Male) / P(Male)

= 0.38 / (0.38+0.13)

= 0.7451

c)

Event of being large independent of the event of being male?

P(Large) = 0.61

P(Male) = 0.51

P(Large) * P(Male) = 0.61 * 0.51 =0.311 which is not equal to P(Large and Male) = 0.38

Hence the two events are not independent.

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