The odds in favor of an event occurring are the ratioof the probability that the event

Chapter 8, Problem 12

(choose chapter or problem)

The odds in favor of an event occurring are the ratioof the probability that the event will occur to theprobability that the event will not occur. The reciprocalof this ratio represents the odds against the eventoccurring.(a) Six of the marbles in a bag are red. The odds againstchoosing a red marble are 4 to 1. How many marblesare in the bag?(b) A bag contains three blue marbles and sevenyellow marbles. What are the odds in favor ofchoosing a blue marble? What are the odds againstchoosing a blue marble?(c) Write a formula for converting the odds in favor ofan event to the probability of the event.(d) Write a formula for converting the probability of anevent to the odds in favor of the event.