Fifty students in the third-grade class listed their hair and eye colors in the table below: Brown hair Blonde hair Total Blue eyes 14 8

Question

Fifty students in the third-grade class listed their hair and eye colors in the table below: Brown hair Blonde hair Total Blue eyes 14 8 22 Brown eyes 16 12 28 30 20 50 Are the events “blonde hair” and “blue eyes” independent?
A) Yes, P(blonde hair) • P(blue eyes) = P(blonde hair ∩ blue eyes)
B) Yes, P(blonde hair) • P(blue eyes) ≠ P(blonde hair ∩ blue eyes)
C) No, P(blonde hair) • P(blue eyes) = P(blonde hair ∩ blue eyes)
D) No, P(blonde hair) • P(blue eyes) ≠ P(blonde hair ∩ blue eyes)

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Answers ( No )

    0
    2021-09-09T16:05:58+00:00

    If two events A and B are independent, then P(A)*P(B) = P(A∩B).  
    P(A) is the probability of being blonde.
    P(B) is the probability of having blue eyes.
    P(A∩B) is the probability of being blonde with blue eyes.

    P(A)*P(B) = (20/50)*(22/50) = 440/2500 = 22/125.
    P(A∩B) = 8/50.
    These two probabilities are not equivalent; 22/125=0.176, while 8/50=0.16.  Our answer is D.

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