Question

A bag contains 20 red marbles and 30 green marbles. What is the probability of getting exactly 10 red marbles and 10 green marbles in a sample of size 20 if the sampling is done without replacement?

Answer 1

Given that, number of red marbles = 20 and

number of green marbles = 30

Total number of marbles = 20 + 30 = 50

20 marbles can be selected from the 50 marbles by, ⁵⁰C₂₀ ways.

And 10 red marbles can be selected from the 20 red marbles by,

²⁰C₁₀ ways and 10 green marbles can be selected from the 30 green marbles by, ³⁰C₁₀ ways.

Therefore, the probability of getting exactly 10 red marbles and 10 green marbles in a sample of size 20 if the sampling is done without replacement is,

Hence, required probability is 0.117783

Note : Excel Command to find, above probability is,

= COMBIN(20, 10) * COMBIN(30, 10) / COMBIN(50, 20)

= 0.117783