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# Entomologist: Insects and Pheromone

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 towards it rather than towards 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 towards the pheromone or towards the control.

Suppose five insects are released.

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

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

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

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

#### Solution Preview

We begin by listing all the possible occurrences. We label the intersects A B C D and E

0 towards the pheromone (1 possibility)

1 towards the pheromone (5 possibilities)

A towards, B towards, C towards, D towards, E towards. (if you know combinatorics, this is simply 5C1)

2 towards the pheromone (10 possibilities)

AB, AC, AD, AE, BC, BD, BE, ...

#### Solution Summary

An entomologist studies effect of a chemical sex attractant (pheromone) on insects are examined.

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