Two bad eggs are mixed accidentally with 10 good one. Find the probability distribution of the number of bad eggs in 3, drawn at random, from this lot.

Solution

Total number of eggs = 12
Number of good eggs = 10
∴ number of bad eggs = 2
Let X denote the random variable. X takes the values 0, 1, 2.
$straight P left parenthesis straight X space equals space 0 right parenthesis space equals space 10 over 12 cross times 9 over 11 cross times 8 over 10 equals 12 over 22 straight P left parenthesis straight X space equals space 1 right parenthesis space equals space 2 over 12 cross times 10 over 11 cross times 9 over 10 plus 10 over 12 cross times 2 over 11 cross times 9 over 10 plus 10 over 12 cross times 9 over 11 cross times 2 over 10 space space space space space space space space space space space space space space space space space space equals space 3 over 22 plus 3 over 22 plus 3 over 22 space equals 9 over 22 straight P left parenthesis straight X space equals space 2 right parenthesis space equals space 2 over 12 cross times 1 over 11 cross times 10 over 10 plus 2 over 12 cross times 10 over 11 cross times 1 over 10 plus 10 over 12 cross times 2 over 11 cross times 1 over 10 space space space space space space space space space space space space space space space space space space equals space 1 over 66 plus 1 over 66 plus 1 over 66 space equals space 1 over 22$
∴ probability distribution table is

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Probability

Two bad eggs are mixed accidentally with 10 good one. Find the probability distribution of the number of bad eggs in 3, drawn at random, from this lot.

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