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:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → P(X) = 7/15, 7/15, 1/15 for X = 0, 1, 2
There are 10 eggs, 3 bad (B) and 7 good (G). Drawing without replacement changes the counts for the second draw.
X = 0 (both good):
\( \displaystyle P(X = 0) = \frac{7}{10} \times \frac{6}{9} = \frac{42}{90} = \frac{7}{15} \)
X = 1 (one bad, in either order, BG or GB):
\( \displaystyle P(X = 1) = \frac{3}{10} \times \frac{7}{9} + \frac{7}{10} \times \frac{3}{9} = \frac{42}{90} = \frac{7}{15} \)
X = 2 (both bad):
\( \displaystyle P(X = 2) = \frac{3}{10} \times \frac{2}{9} = \frac{6}{90} = \frac{1}{15} \)
Check: \(\frac{7}{15} + \frac{7}{15} + \frac{1}{15} = 1\).
CBSE Applied Mathematics (Class XII):
Mathematical Expectation of Discrete Probability Distribution
