Can anyone show me how to do probabilities? I\'m struggling and especially confu

ID: 3127409 • Letter: C

Question

Can anyone show me how to do probabilities? I'm struggling and especially confused which equations to use. Thanks!

Probability

Dark Hair Light Hair Brown eyes 300 420 Blue eyes 200 1270

a) If one individual is selected at random from this population, what is the probability that he will have dark hair?

b) What is the probability that he will have dark hair OR blue eyes OR both?

c) What is the probability that he will have blue eyes given that we know he will have dark hair?

d) Is having dark hair independent of having blue eyes? explain.

Dark hair Light hair Brown eyes 300 420 Blue eyes 200 1270

a.) P(dark hair) = (300 + 200)/2190 = 0.2283

b.) P( dark hair or blue eyes or both)

= P(dark hair) + P(blue eyes) + P( dark hair and blue eyes)

= 500/2190 + 1470/2190 + 200/2190

= 0.9909

c.) P(blue eyes | he has dark hair)

= P( he has blue eyes and dark hair)/P( he has dark hair)

= (200/2190) /(500/2190)

= 0.4

d.) P( dark hair and blue eyes) = 200/2190

P(dark hair ) = 500/2190

P(blue eyes) = 1470/2190

P( dark hair ) × P(blue eyes) P(dark hair and blue eyes)

Therefore having dark hair is not independent of having blue eyes.

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.