Questions: (a) Leila is playing a game on her smartphone. She will choose an image to see if she gets bonus points. The probability of getting bonus points is 8/19. Find the odds in favor of getting bonus points. (b) The manager of a restaurant determined that the odds against a customer ordering dessert are 11/2. What is the probability of a customer ordering dessert?

Solution Steps

We need to convert between probability and odds. The first question asks for the odds in favor of an event given its probability. The second question asks for the probability of an event given the odds against it.

The probability of getting bonus points is given as \( \frac{1}{9} \). The odds in favor of an event are calculated as the ratio of the probability of the event occurring to the probability of the event not occurring.

\[ \text{Odds in favor} = \frac{P(\text{event})}{1 - P(\text{event})} \]

Substitute \( P(\text{event}) = \frac{1}{9} \):

\[ \text{Odds in favor} = \frac{\frac{1}{9}}{1 - \frac{1}{9}} = \frac{\frac{1}{9}}{\frac{8}{9}} = \frac{1}{8} \]

The odds against a customer ordering dessert are given as \( \frac{11}{2} \). The probability of an event given the odds against it is calculated as:

\[ \text{Probability} = \frac{1}{1 + \text{Odds against}} \]

Substitute \( \text{Odds against} = \frac{11}{2} \):

\[ \text{Probability} = \frac{1}{1 + \frac{11}{2}} = \frac{1}{\frac{2}{2} + \frac{11}{2}} = \frac{1}{\frac{13}{2}} = \frac{2}{13} \]

Final Answer