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)
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 |
A box contains seven marbles. Four of them are red and 3 of them are green....
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