Question

use the table below to answer the questions.
if a student is randomly selected, what is the probability they are a girl?
if a student is randomly selected, what is the probability they are a boy that can bike to school?
if a student is randomly selected, what is the probability they are a girl or can bike to school?
given that a randomly selected student is a boy, what is the probability they can bike to school?

Explanation:

Step1: Probability of selecting a girl

The formula for probability is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
The number of girls is \(19\) and the total number of students is \(30\). So \(P(\text{girl})=\frac{19}{30}\).

Step2: Probability of selecting a boy that can bike

The number of boys that can bike is \(7\) and the total number of students is \(30\). So \(P(\text{boy and can bike})=\frac{7}{30}\).

Step3: Probability of selecting a girl or can bike

Use the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\).
\(P(\text{girl})=\frac{19}{30}\), \(P(\text{can bike})=\frac{16}{30}\), \(P(\text{girl and can bike})=\frac{9}{30}\).
\(P(\text{girl or can bike})=\frac{19 + 16-9}{30}=\frac{26}{30}=\frac{13}{15}\).

Step4: Conditional probability (given a boy, probability can bike)

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\).
Here \(A\) is “can bike” and \(B\) is “is a boy”. \(P(\text{boy and can bike})=\frac{7}{30}\), \(P(\text{boy})=\frac{11}{30}\). So \(P(\text{can bike}|\text{boy})=\frac{7}{11}\).

Answer:

\(\frac{19}{30}\), \(\frac{7}{30}\), \(\frac{13}{15}\), \(\frac{7}{11}\)