A box contains 2 white and 2 black balls

MATHEMATICS · Single correct · AP · AP Statistics · Probability Random Variables Distributions · Probability Random Variables Distributions

Problem

A box contains 2 white and 2 black balls. A ball is drawn, replaced, and the box is shaken before drawing a second ball. Let A be the event "the first ball drawn is white" and B be the event "the second ball drawn is black". Which of the following statements is correct? (a) P(B∣A)=12,  so A and B are independentP(B\mid A)=\tfrac12,\; \text{so }A \text{ and }B \text{ are independent} (b) P(B∣A)=23,  so A and B are dependentP(B\mid A)=\tfrac23,\; \text{so }A \text{ and }B \text{ are dependent} (c) P(B∣A)=14,  so A and B are independentP(B\mid A)=\tfrac14,\; \text{so }A \text{ and }B \text{ are independent} (d) P(B∣A)=12,  so A and B are dependentP(B\mid A)=\tfrac12,\; \text{so }A \text{ and }B \text{ are dependent}

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