Question

the table shows the educational attainment of the population of a certain country, ages 25 and over, expressed in millions. find the probability that a randomly selected person, aged 25 or over, has completed four years of high school only or is male.

	years of high school		years of college		total
	less than 4	4 only	some (less than 4)	4 or more
male	11	29	22	16	78
female	11	33	23	23	90
total	22	62	45	39	168

the probability is \boxed{}. (type an integer or a simplified fraction.)

Explanation:

Step1: Identify values for formula

Let \( A = \text{4 years of high school only} \), \( B = \text{male} \). Total population \( N = 168 \), \( n(A) = 62 \), \( n(B) = 78 \), \( n(A \cap B) = 29 \).

Step2: Apply addition rule

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

Step3: Calculate numerator

\( 62 + 78 - 29 = 111 \)

Step4: Simplify fraction

\( \frac{111}{168} = \frac{37}{56} \)

Answer:

\(\frac{37}{56}\)