An experiment has only two possible outcomes. The first outcome occurs with probability $p$ and the second outcome occurs with probability $p^2$ . Find the value of $p$ , correct to 3 decimal places.

Model answer

0.618

Explanation

Since the two probabilities must sum to 1,

p+p^2=1

, i.e.

p^2+p-1=0

. By the quadratic formula,

p=\frac{-1+\sqrt5}{2}\approx0.618

(the negative root is rejected since a probability cannot be negative).

Derived from ZIMSEC Statistics Paper 4, June 2009, Q1

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