the accompanying table shows the numbers of male and female students in a particular country who received…

the accompanying table shows the numbers of male and female students in a particular country who received bachelors degrees in business in a recent year. complete parts (a) and (b) below. click the icon to view the data on business degrees. (a) find the probability that a randomly selected student is male, given that the student received a business degree. the probability that a randomly selected student is male, given that the student received a business degree, is 0.541. (round to three decimal places as needed.) (b) find the probability that a randomly selected student received a business degree, given that the student is female. the probability that a randomly selected student received a business degree, given that the student is female, is 0.459. (round to three decimal places as needed.) business graduates business degrees non - business degrees total male 193,910 623,198 817,108 female 164,659 925,653 1,090,312 total 358,569 1,548,851 1,907,420

the accompanying table shows the numbers of male and female students in a particular country who received bachelors degrees in business in a recent year. complete parts (a) and (b) below. click the icon to view the data on business degrees. (a) find the probability that a randomly selected student is male, given that the student received a business degree. the probability that a randomly selected student is male, given that the student received a business degree, is 0.541. (round to three decimal places as needed.) (b) find the probability that a randomly selected student received a business degree, given that the student is female. the probability that a randomly selected student received a business degree, given that the student is female, is 0.459. (round to three decimal places as needed.) business graduates business degrees non - business degrees total male 193,910 623,198 817,108 female 164,659 925,653 1,090,312 total 358,569 1,548,851 1,907,420

Answer

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of elements in the intersection of $A$ and $B$, and $n(B)$ is the number of elements in $B$.

Step2: Calculate probability for part (a)

We want to find $P(\text{Male}|\text{Business degree})$. Here, $n(\text{Male}\cap\text{Business degree}) = 193910$ (number of male business - degree holders) and $n(\text{Business degree})=358569$ (total number of business - degree holders). So $P(\text{Male}|\text{Business degree})=\frac{193910}{358569}\approx0.541$.

Step3: Calculate probability for part (b)

We want to find $P(\text{Business degree}|\text{Female})$. Here, $n(\text{Female}\cap\text{Business degree}) = 164659$ (number of female business - degree holders) and $n(\text{Female}) = 1090312$ (total number of female students). So $P(\text{Business degree}|\text{Female})=\frac{164659}{1090312}\approx0.459$.

Answer:

(a) $0.541$ (b) $0.459$