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:

The correct answer is Option (3) → 

Total eggs = 3 bad + 7 good = 10 eggs

Draw 2 eggs without replacement

Random variable X = number of bad eggs drawn

P(X=0): Both eggs are good

$P(X=0) = \frac{7}{10} \cdot \frac{6}{9} = \frac{42}{90} = \frac{7}{15}$

P(X=1): One bad and one good (two orders)

$P(X=1) = \frac{3}{10} \cdot \frac{7}{9} + \frac{7}{10} \cdot \frac{3}{9} = \frac{21}{90} + \frac{21}{90} = \frac{42}{90} = \frac{7}{15}$

P(X=2): Both eggs are bad

$P(X=2) = \frac{3}{10} \cdot \frac{2}{9} = \frac{6}{90} = \frac{1}{15}$

Probability distribution:

$X = 0 \; : \; \frac{7}{15}$

$X = 1 \; : \; \frac{7}{15}$

$X = 2 \; : \; \frac{1}{15}$