Answer:
(a) Shown in table.
(b) All the probabilities add up to be 1.
(c) Sample space is, S = {0, 1, 2, 3, 4}
Step-by-step explanation:
Let X = number of similar preference.
The formula to compute the probability of an event E is,
[tex]P(E)=\frac{n(E)}{N}[/tex]
Here,
n (E) = favorable outcomes of event E
N = total number of outcomes.
(a)
Compute the probability that a randomly selected married couple has 0 similar preference as follows:
[tex]P(X = 0)=\frac{39}{375}=0.104[/tex]
Compute the probability that a randomly selected married couple has 1 similar preference as follows:
[tex]P(X = 1)=\frac{69}{375}=0.184[/tex]
Compute the probability that a randomly selected married couple has 2 similar preference as follows:
[tex]P(X = 2)=\frac{110}{375}=0.293[/tex]
Compute the probability that a randomly selected married couple has 3 similar preference as follows:
[tex]P(X = 3)=\frac{122}{375}=0.325[/tex]
Compute the probability that a randomly selected married couple has 4 similar preference as follows:
[tex]P(X = 2)=\frac{35}{375}=0.093[/tex]
(b)
Compute the sum of all probabilities as follows:
[tex]\sum P (X=x)=P (X=0)+P (X=1)+P (X=2)+P (X=3)+P (X=4)\\=0.104+0.184+0.293+0.325+0.093\\=0.999\\\approx1[/tex]
All the probabilities add up to be 1.
According to the probability distribution, all the probabilities of every sample space value must add up to 1.
(c)
The sample space in this case be defined as the number of similar preference married couples have.
S = {0, 1, 2, 3, 4}
