In a certain corporation, there are 300 male employees and

AAPL wrote:Magoosh

In a certain corporation, there are 300 male employees and 100 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree or is female?

A. 1/20
B. 1/10
C. 1/5
D. 2/5
E. 3/4

OA D

20% of the 300 male employees have advanced degrees and 40% of the 100 females have advanced degrees
20% of 300 = 60. So, there are 60 MALES with advanced degrees
40% of 100 = 40. So, there are 40 FEMALES with advanced degrees
Total number of advanced degrees = 60 + 40 = 100
So, P(selected person has advanced degree) = 100/400 = 1/4
Also, P(selected person is female AND has a advanced degree) = 40/400 = 1/10
Also, P(selected person is female) = 100/400 = 1/4

What is the probability the selected employee has an advanced degree or is female?
P(A or B) = P(A) + P(B) - P(A and B)
So, P(employee has advanced degree OR employee is female) = P(employee has advanced degree) + P(employee is female) - P(selected person is female AND has a advanced degree)
= 1/4 + 1/4 - 1/10
= 2/4 - 1/10
= 2/5

Answer: D

Cheers,
Brent

AAPL wrote:Magoosh

In a certain corporation, there are 300 male employees and 100 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree or is female?

A. 1/20
B. 1/10
C. 1/5
D. 2/5
E. 3/4

OA D

Since 20% of the male employees have advanced degrees, 0.2 x 300 = 60 male employees have advanced degrees, and 300 - 60 = 240 male employees do not have advanced degrees.

Since 40% of the female employees have advanced degrees, 0.4 x 100 = 40 female employees have advanced degrees and 100 - 40 = 60 female employees do not have advanced degrees.

So, 60 + 40 = 100 employees have an advanced degree.

Thus, the probability of selecting an employee who is female or has an advanced degree is:

P(woman) + P(advanced) - P(both)

100/400 + 100/400 - 40/400

160/400 = 16/40 = ⅖

Alternate Solution:

The only way an employee is not a female or does not have an advanced degree is if the employee is a male without an advanced degree. Since 20% of the males have advanced degrees, 80% have no advanced degrees, and thus, there are 300 x 0.8 = 240 males without advanced degrees. Therefore, 400 - 240 = 160 remaining employees meet the criteria, and thus, the probability of choosing an employee who is either female or has an advanced degree is 160/400 = 2/5.

Answer: D