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Probability

Probability

IP 4

Two fair six-sided dice are rolled. Let
\[ A=\{\text{sum is greater than}\hspace{0.5em}8\},\qquad B=\{\text{first die shows an even number}\hspace{0.15em}\}. \]

  1. Find \(P(A\mid B)\) by counting suitable ordered pairs.

  2. Find \(P(B\mid A)\).

  3. Explain why the answers need not be equal.

Solution:

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Answer:(a) \(\frac13\). (b) \(\frac35\). (c) The conditioning groups differ, so the denominators differ.

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