Question

There are 200 blue balls and 10 red balls in an urn. Suppose that 10 balls are taken random;ly from the urn and let X denote the number of red balls selected.

a) The distribution of the random variable X is___.
i) Binomial.
ii) Hypergeometric.
iii) Poisson.
iv) Normal.
v) Exponential.
vi) Uniform
b) Find P(all 10 balls are red).
c) Which distribution from those listed in part (a) can be used as an approximation to the distribution of X? With this approximation find P(X = 10).

Answer 1

Hypergeometric

Kindly check explanation

Explanation:

For a hypergeometric distribution, the following conditions must be met :

1.) The total number of samples must be fixed.

2.) Sample size will be a portion of the population

3.) The probability of success changes per trial. This is because sampling is done without replacement

The above scenario meets the condition described:

Total number of samples = 210

Sample size, n = 10

Blue balls = 200 ; red balls = 10

P(10 red balls)

Using the hypergeometric distribution function and the calculator :

X ~ H(n, N, M)

X ~ (10, 200, 210) = 0.6072