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) →
|
X |
0 |
1 |
2 |
|
P(X) |
7/15 |
7/15 |
1/15 |
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:
$X = 0 \; : \; \frac{7}{15}$
$X = 1 \; : \; \frac{7}{15}$
$X = 2 \; : \; \frac{1}{15}$