Question

fill in the blank 3 points
use the bivariate table to answer the following questions.
find the probability that the student is female given the student is a nursing major.
(round to the nearest thousandth as needed)
type your answer...
find the probability that the student is male and a nursing major.
(round to the nearest thousandth as needed)
type your answer...
find the probability that he is male or a nursing major.
(round to the nearest thousandth as needed)
type your answer...

Explanation:

First Question: Probability that the student is female given the student is a nursing major

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of a contingency table, for \(A\) = "female" and \(B\) = "nursing major", \(P(A|B)=\frac{\text{Number of female - nursing majors}}{\text{Total number of nursing majors}}\).

Step2: Substitute the values from the table

From the table, the number of female - nursing majors is \(600\) and the total number of nursing majors is \(698\). So, \(P=\frac{600}{698}\approx 0.860\).

Second Question: Probability that the student is male and a nursing major

Step1: Use the formula for joint probability

The formula for joint probability in a contingency table is \(P(A\cap B)=\frac{\text{Number of elements in }A\cap B}{\text{Total number of elements}}\). Here, \(A\) = "male" and \(B\) = "nursing major". The number of male - nursing majors is \(98\) and the total number of students is \(3437\). So, \(P=\frac{98}{3437}\approx 0.029\).

Third Question: Probability that the student is male or a nursing major

Step1: Recall the formula for the probability of the union of two events

The formula is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\).

• \(P(A)\) (probability of being male) is \(\frac{1113}{3437}\)
• \(P(B)\) (probability of being a nursing major) is \(\frac{698}{3437}\)
• \(P(A\cap B)\) (probability of being male and a nursing major) is \(\frac{98}{3437}\)

Step2: Substitute the values

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Answer:

1. \(0.860\)
2. \(0.029\)
3. \(0.498\)