Question

From an urn that contains only 7 orange balls and 3 blue balls, take a random sample of 2 balls without replacement. Let the random variable X be the number of orange balls in the sample. Find P(X = 0). Give your answer to 4 decimal places.

Answer 1

Solution:
Here we will use hypergeometric distribution for which probability can be calculated as
P(X= x |n,N,A) = (ACx)*((N-A)C(n-x))/NCn
Here 7 orange ball and 3 blue balls so total number of balls or population size (N)= 7+3 = 10 balls
Sample size(n) = 2
Number of events of interest in the population i.e. Number of orange balls(A) = 7
Number of events of interest in the sample(x) = 0
So P(X=) can be calculated as
P(X= x |n,N,A) = (ACx)*((N-A)C(n-x))/NCn = (7C0)*((10-7)C(2-0))/(10C2) = 1*3/45 = 0.0667
So there is 6.67% probability that numver of orange balls in the sample is 0.