Three bad eggs are mixed with 7 good ones. If two eggs are drawn one by one without replacement, then the probability distribution of the number (X) of bad eggs drawn is:

X	0	1	2
P(X)	1/4	1/2	1/4

X	0	1	2
P(X)	15/61	20/61	26/61

X	0	1	2
P(X)	7/15	7/15	1/15

X	0	1	2
P(X)	1/8	1/4	5/8

There are 3 bad eggs and 7 good eggs, for a total of 10 eggs. Two eggs are drawn one by one without replacement.

X represents the number of bad eggs drawn. X can be 0, 1, or 2.

For X = 0, both eggs drawn are good.

First egg is good: $\frac{7}{10}$

Second egg is good: $\frac{6}{9}$

$P(X = 0) = \frac{7}{10} \times \frac{6}{9}$

$P(X = 0) = \frac{42}{90}$

$P(X = 0) = \frac{7}{15}$

For X = 1, exactly one bad egg is drawn. This occurs in two ways:

Bad egg first, then good egg:

$\frac{3}{10} \times \frac{7}{9} = \frac{21}{90}$

Good egg first, then bad egg:

$\frac{7}{10} \times \frac{3}{9} = \frac{21}{90}$

$P(X = 1) = \frac{21}{90} + \frac{21}{90}$

$P(X = 1) = \frac{42}{90}$

$P(X = 1) = \frac{7}{15}$

For X = 2, both eggs drawn are bad.

First egg is bad: $\frac{3}{10}$

Second egg is bad: $\frac{2}{9}$

$P(X = 2) = \frac{3}{10} \times \frac{2}{9}$

$P(X = 2) = \frac{6}{90}$

$P(X = 2) = \frac{1}{15}$

The probability distribution is:

This corresponds to Option 3.