for two programs at a university, the type of student for two majors is as follows.\n| | history | science |…

for two programs at a university, the type of student for two majors is as follows.\n| | history | science | total |\n|--|--|--|--|\n| undergraduate | 390 | 422 | 812 |\n| graduate | 73 | 188 | 261 |\n| total | 463 | 610 | 1073 |\nfind the probability a student is a history major, given they are a undergraduate student.\np(history | undergrad) = \\frac{p(history and undergrad)}{p(undergrad)} = ?\nround to the nearest hundredth.

for two programs at a university, the type of student for two majors is as follows.\n| | history | science | total |\n|--|--|--|--|\n| undergraduate | 390 | 422 | 812 |\n| graduate | 73 | 188 | 261 |\n| total | 463 | 610 | 1073 |\nfind the probability a student is a history major, given they are a undergraduate student.\np(history | undergrad) = \\frac{p(history and undergrad)}{p(undergrad)} = ?\nround to the nearest hundredth.

Answer

Explanation:

Step1: Identify relevant values

$P(\text{history and undergrad})=\frac{390}{1073}$, $P(\text{undergrad})=\frac{812}{1073}$

Step2: Apply conditional - probability formula

$P(\text{history}|\text{undergrad})=\frac{P(\text{history and undergrad})}{P(\text{undergrad})}=\frac{\frac{390}{1073}}{\frac{812}{1073}}=\frac{390}{812}$

Step3: Calculate the result

$\frac{390}{812}\approx0.48$

Answer:

$0.48$