In a group of 25 persons, 4 are left-handed. Suppose that two persons are random

Question

In a group of 25 persons, 4 are left-handed. Suppose that two persons are randomly selected from this group. Let x denote the number of left-handed persons in this sample. Choose the correct probability distribution of x. (Hint: Note that the draws are made without replacement from a small population. Hence, the probabilities of outcomes do not remain constant for each draw.)

x

0

1

2

P(x)

425

1925

225

x

0

1

2

P(x)

425

125

2025

x

0

1

2

P(x)

399600

189600

12600

x

0

1

2

P(x)

420600

168600

12600

x

0

1

2

P(x)

225

1925

425

x

0

1

2

P(x)

425

1925

225

Explanation / Answer

in a group of 25 persons 4 are left handed and 21 are right handed, 2 are selected at random

if x denotes the number of left-handed persons

then, x is a random variable which can take values 0,1,2

hence, P(X=0) = 21C2 / 25C2 = 210 / 300 = 420 / 600

P(X=1) = 21C14C1 / 25C2 = 84 / 300 = 168 / 600

P(X=2) = 4C2 / 25C2 = 6 / 300 = 12 / 600

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