Question

A box contains seven marbles. Four of them are red and 3 of them are green. You reach in and choose three at random without replacement. Define a random variable X as: X = the number of red marbles selected.

(a) What are the possible values X can take on? (i.e. give Im(X))

(b) Find P(X = x) for all x in Im(X).

(c) Make a table for the probability distribution of X as shown in lecture. (Leave probabilities as fractions)

Answer 1

a) As we are choosing 3 marbles out of the 7 marbles, the number of red marbles ranges from 0 to 3 as 3 are selected. Therefore the sample space for X here is given as:
X = { 0, 1, 2, 3 }

b) The probabilities here are computed as:

P(X = x) = Number of ways to select x red marbles from 4 red marbles * Number of ways to select (3-x) green marbles from 3 green marbles / Total ways to select 3 marbles out of the 7 marbles

Therefore the probabilities now are computed here as:

This is the required PMF for X here.

c) The probability table is given as:

X	P(X = x)
0	1/35
1	12/35
2	18/35
3	4/35