Question

The table below shows a random sample of musicians and how they learned to play their instruments.





Part A

Find P(musician is a female). Write your answer as a fraction into the box below.

72
130​
(b)
Part B

Find P(musician is a female OR is self taught). Write your answer as a fraction into the box below.

(c)
Part C

Find P(male | studied in school). Write your answer as a fraction into the box below.

Answer 1

I don't have the full table you mentioned, but I can finish Part A from the numbers you gave and tell you exactly how to do Parts B and C once you supply the table entries.

Part A
You gave 72 out of 130: P(musician is female) = 72/130 = 36/65.

Part B (female OR self-taught)
Use the inclusion–exclusion formula:
P(female OR self‑taught) = (number female + number self‑taught − number who are both female and self‑taught) / total.
So if you tell me the counts for (a) total self‑taught and (b) female & self‑taught, I will compute the fraction and simplify it.

Part C (male | studied in school)
This is a conditional probability:
P(male | studied in school) = (number of males who studied in school) / (total number who studied in school).
Give me the two counts from the table and I will give the fraction simplified.

If you paste the full table (or the counts for self‑taught, studied in school, and the male/female breakdowns), I’ll compute Parts B and C exactly.