Question

Five years after 650 high school seniors graduated, 400 had a college degree and 310 were married. Half of the students with a college degree were married. What is the probability that a student has a college degree or is not married

Answer 1

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,

$P(E)=\frac{n(E)}{N}$

Here,

n (E) = favorable outcomes of E

N = total number of outcomes of the experiment.

The probability of the union of two events is:

$P(A\cup B)=P(A)+P(B)-P(A\cap B)=\frac{n(A)+n(B)-n(A\cap B)}{N}$

Compute the probability that a student has a college degree or is not married as follows:

$P(C\cup M^{c})=\frac{n(C)+n(M^{c})-n(C\cap M^{c})}{N}$

From the Venn diagram:

n (C) = 400

n ($M^{c}$) = N - n (M) = 650 - 310 = 340

n (C ∩ $M^{c}$) = 200

The value of P (C ∪ $M^{c}$) is:

$P(C\cup M^{c})=\frac{n(C)+n(M^{c})-n(C\cap M^{c})}{N}=\frac{400+340-200}{650}=0.83077\approx0.8308$

Thus, the probability that a student has a college degree or is not married is 0.8308.

Answer 2

Answer: 2/34

Step-by-step explanation:

2/34 chance