Question

The students at a certain high school have an elective period, where each student chooses an elective from among four options. The following table shows the number of students who selected each elective for the 1,500 students at the high school.
Art Music Physical Education Engineering Total
385 365 380 370 1,500
One student from the school will be selected at random. What is the probability the selected student chose the art elective and the music elective?

Answer 1

Answer:

0.0625

Step-by-step explanation:

Total Number of Students, n(S) =1500

Number of Art Students, n(A)=385

Number of Music Students, n(M)=365

$P(A)=\dfrac{n(A)}{n(S)} =\dfrac{385}{1500} =\dfrac{77}{300}\\P(M)=\dfrac{n(M)}{n(S)} =\dfrac{365}{1500} =\dfrac{73}{300}$

In probability theory, P(A and B)=P(A) X P(B), therefore the probability that the student chose the art AND music elective

P(A and M)=P(A) X P(M)

$=\dfrac{77}{300}X\dfrac{73}{300}\\=\dfrac{5621}{90000}\\=0.0625$