I need some help with this geometry question!

Question

A school finds that 62% of its students play a sport and 20% of its students play a sport and an instrument. Find the probability a plays an instrument, given they play a sport.

Answer 1

The probability a student plays an instrument, given they play a sport, is approximately 0.3226 or 32.26%.

Variables:

A = student plays an instrument

B = student plays a sport

Given:

P(B) = 0.62, students play a sport

P(A ∩ B) = 0.20, students play both a sport and an instrument

Conditional probability:

P(A | B) = P(A ∩ B) / P(B)

Substitute and simplify:

P(A | B) = 0.20 / 0.62

= 0.3226

Answer 2

P(s)= .62, P(s^i) = .2, P(i/s)=?

draw a Venn diagram (is that why it's posted as "geometry"?)

or

P(i/s) = P(s^i)/P(s) = .2/.62 = 20/62 = 10/31

= about 0.32258065