Multiple choice

The chance of happening of an event is the square of the chance of happening of the second event, but the odds against the first are the cube of the odds against the second. Find the chances of the events.

  1. 1/2, 1/4

  2. 1/3, 1/9

  3. 2/3, 4/3

  4. 1/4, 1/16
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B Correct answer
AI explanation

Let the chances of the first and second events be p1 and p2, so we have p1 equals p2 squared. The odds against the first and second events are (1 minus p1) divided by p1 and (1 minus p2) divided by p2 respectively, leading to the equation (1 minus p1) divided by p1 equals ((1 minus p2) divided by p2) cubed. Substituting p1 equals p2 squared into the second equation and solving for p2 yields p2 equals 1/3. Substituting p2 equals 1/3 into the first equation gives p1 equals 1/9. Therefore, the chances of the events are 1/3 and 1/9.

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