A committee of 5 is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all is:
Step-by-step Solution:
Let the total number of ways to choose a married couple together be denoted as: \[ \text{Total ways} = \binom{7}{3}. \] If the married couple is not included, the number of ways is: \[ \text{Ways where couple is not included} = \binom{7}{5}. \] The probability \( P(E) \) of event \( E \) (where the couple is included) is given by: \[ P(E) = \frac{\binom{7}{3} + \binom{7}{5}}{\binom{9}{5}}. \] Simplifying: \[ P(E) = \frac{4}{9}. \]