Question

According to a study, 38% of experienced file-sharers with broadband access had decreased their spending on music. Let us estimate that 3% of all music fans were experienced file-sharers with broadband access at the time of the study. If 25% of the other music fans had decreased their spending on music, what percentage of those who had decreased their spending on music were experienced file-sharers with broadband access

Answer 1

0.0449

The required percentage = 4.49%

Explanation:

38% experienced filesharers decreased spending

3% of music fans have broadband access

25% of other fans have reduced spending

A = event that fan is a file sharer and has broadband access

B = event that fan has decreased spending on music

P(B|A) = 0.38

P(A) = 0.03

P(B|A') = 0.25

To answer this question I used bayes theorem.

[P(B|A).P(A)] / [P(B|A).P(A) + P(B|A').P(A')]

= 0.38x0.03/(0.38x0.03) + 0.25(1-0.03)

= 0.0114/0.114+0.2425

= 0.0114/0.2539

= 0.0449

Therefore the required percentage is 4.49% or 4.5%