Chemical insect attractant. An entomologist is studying the effect of a chemical sex attractant (pheromone) on insects.

Several insects are released at a site equidistant from the pheromone under study and a control substance. If the pheromone has an effect, more insects will travel toward it rather than toward the control. Otherwise, the insects are equally likely to travel in either direction. Suppose the pheromone under study has no effect, so that it is equally likely that an insect will move toward the pheromone or toward the control. Suppose four insects are released.

a. List or count the number of different ways the insects can travel.

b. What is the chance that all four travel toward the pheromone?

c. What is the chance that exactly three travel toward the pheromone?

d. What inference would you make if the event in part c actually occurs? Explain.