firstborn AND a nursing student

I will rate and comment, please answer all questions below A survey of students in a…

I will rate and comment, please answer all questions below

A survey of students in a large intro to Statistics class asked about their birth order (1 = oldest or only child) and which course of study at the university they were enrolled in. Suppose we select a student at random from this class.

1 or Only 2 or more    Total
English      37      23 60
Science and Engineering      52      41 93
Nursing      29      21 50
Other      12      18 30
Total 130 103 233

What is the probability that the student is (please give the faction and the decimal rounded to 3 decimal places)

a. a first-born student?

b. firstborn AND a nursing student?

c. firstborn OR a nursing student?

d. Given that a student is first born, what is the probability that they are a nursing student?

e. Are course of study and birth order independent events? Explain using the independence formula