at a local college, 100 students were asked about their major fields of study. the results are shown below…

at a local college, 100 students were asked about their major fields of study. the results are shown below. what is the probability that a randomly selected student is a female or a liberal arts major? majors at local college mathematics/science liberal arts business studies male 16 20 14 female 15 18 17

at a local college, 100 students were asked about their major fields of study. the results are shown below. what is the probability that a randomly selected student is a female or a liberal arts major? majors at local college mathematics/science liberal arts business studies male 16 20 14 female 15 18 17

Answer

Explanation:

Step1: Calculate number of females

Add the number of females in each major. $15 + 18+17=50$.

Step2: Calculate number of liberal - arts majors

Add the number of male and female liberal - arts majors. $20 + 18 = 38$.

Step3: Calculate number of female liberal - arts majors

The number of female liberal - arts majors is 18.

Step4: Use the addition rule for probability

The formula for $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, $A$ is the event of being a female and $B$ is the event of being a liberal - arts major. The total number of students is $n = 100$. $P(A)=\frac{50}{100}$, $P(B)=\frac{38}{100}$, $P(A\cap B)=\frac{18}{100}$. $P(A\cup B)=\frac{50 + 38-18}{100}=\frac{70}{100}=\frac{7}{10}$.

Answer:

$\frac{7}{10}$