Sample Space and probability

Question

Gerardo spins a spinner with four equal sections, labeled A, B, C, and D, twice. If letter A is spun at least once, Gerardo wins. Otherwise, Odell wins. Use a list to find the sample space. Then find the probability that Odell wins

Answer 1

The possible results are:

    First Spin      Second Spin

   -----------      --------------

        A                    A         Geraldo wins

        A                    B         Geraldo wins

        A                    C         Geraldo wins

        A                    D         Geraldo wins

        B                    A         Geraldo wins

        B                    B

        B                    C

        B                    D

        C                    A         Geraldo wins

        C                    B

        C                    C

        C                    D

        D                    A         Geraldo wins

        D                    B

        D                    C

        D                    D

 

The sample space:  There are 16 possible outcomes.

 

Probability is defined as:   (number of successful outcomes) / (number of possible outcomes)

Probability of at least one "A":     7/16   (Geraldo wins)

 

Ah, but, the probability that Odell wins (no letter "A") is:  9/16