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JAMB 2012 · UTME · Q49

The probability that a student passes a physics test is 23\frac23. If he takes three physics tests, what is the probability that he passes two of the tests?

Worked solution (try it first)
  1. One order, pass, pass, fail, has probability 23×23×13=427\frac23 \times \frac23 \times \frac13 = \frac{4}{27}.
  2. The failed test can be the first, second or third, so there are 3 such orders.
  3. So the probability is 3×427=493 \times \frac{4}{27} = \frac{4}{9}, option A.

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