Two ballpoint pens are selected at random from a box that contains 3 blue pens, 2 red pens, and 3 green pens. If X is the number
of blue pens selected and Y is the number of red pens selected, find (a) the joint probability mass function, (b) P [(X, Y ) ∈ A], where A is the region {(x, y)|x + y ≤ 1}.
1 answer:
Answer:
a) f(x,y) =; x = 0, 1, 2; y = 0, 1, 2; 0 ≤ x+y ≥ 2
b) =
Step-by-step explanation:
The joint probability describes how a random variable is distributed. For two random variables, X and Y, the joint probability is expressed as P(X = x, Y = y)
In the context provided,
X = The count of blue pens
Y = The count of red pens
a)
The combinations of (X, Y) are (0, 0), (0, 1), (1, 0), (1, 1), (0, 2), (2, 0)
Refer to the figure as well
The total number of ways to choose any 2 pens = =
=28
f(x,y) = ; x = 0, 1, 2; y = 0, 1, 2; 0 ≤ x+y ≥ 2
b)
P(X,Y)∈A = P(X + Y ≤ 1)
= P(0,0) + P(1,0) + P(0,1)
= +
+
=
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