Respuesta :
Answer:
The probability that a student has a college degree or is not married is 0.8308.
Step-by-step explanation:
The information provided is:
Total number of high school seniors (N) = 650.
Number of seniors with a college degree (n (C)) = 400.
Number of seniors who were married, (n (M)) = 310.
Consider the Venn diagram below.
The probability of an event, say E, is the ratio of the favorable outcomes of E to the total number of outcomes of the experiment.
That is,
[tex]P(E)=\frac{n(E)}{N}[/tex]
Here,
n (E) = favorable outcomes of E
N = total number of outcomes of the experiment.
The probability of the union of two events is:
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)=\frac{n(A)+n(B)-n(A\cap B)}{N}[/tex]
Compute the probability that a student has a college degree or is not married as follows:
[tex]P(C\cup M^{c})=\frac{n(C)+n(M^{c})-n(C\cap M^{c})}{N}[/tex]
From the Venn diagram:
n (C) = 400
n ([tex]M^{c}[/tex]) = N - n (M) = 650 - 310 = 340
n (C ∩ [tex]M^{c}[/tex]) = 200
The value of P (C ∪ [tex]M^{c}[/tex]) is:
[tex]P(C\cup M^{c})=\frac{n(C)+n(M^{c})-n(C\cap M^{c})}{N}=\frac{400+340-200}{650}=0.83077\approx0.8308[/tex]
Thus, the probability that a student has a college degree or is not married is 0.8308.
