Question

Of all college degrees awarded in the United States, including masters and doctorate degrees, 26 % are associate degrees, 40 % are earned by men, and 10 % are associate degrees earned by men. What is the conditional probability that a degree is earned by a man, given that it is an associate degree? (Enter your answer rounded to three decimal places.)

Answer 1

Answer:

0.385 is the required conditional probability.    

Step-by-step explanation:

We are given the following in the question:

Percentage of associated degree = 26%

$P(A)=26\%=0.26$

Percentage of degrees earned by men = 40%

$P(M)=40\%=0.4$

Percentage of associate degrees earned by men = 10%

$P(A\cap M) = 10\% = 0.10$

We have to evaluate the conditional property that a degree is earned by a man, given that it is an associate degree.

$P(M|A) = \dfrac{P(M\cap A)}{P(A)} = \dfrac{0.1}{0.26} = 0.385$

0.385 is the conditional probability that a degree is earned by a man, given that it is an associate degree.

Answer 2

Answer:

Conditional Probability = 0.385

Step-by-step explanation:

Let Percentage of associate degrees = P(AD) = 26%

     Percentage of degrees earned by men = P(M) = 40%

     Percentage of associate degrees earned by men = $P(AD \bigcap M)$ = 10%

Now, conditional probability that a degree is earned by a man, given that it is an associate degree = P(M/AD)

As we know that; P(A/B) = $\frac{P(A\bigcap B)}{P(B)}$

Similarly, P(M/AD) =  $\frac{P(AD\bigcap M)}{P(AD)}$ = $\frac{0.10}{0.26}$

                               = 0.385