Given: A certain insecticide kills 50% of all insects in lab experiments, a sample of 11 insects is exposed to the insecticide in a particular experiment.
Required: To determine the probability that exactly 6 insects will survive.
Step-by-step explanation: The probability of x successes in n trials is:

Where p and q are the probabilities of success and failure.
Here p=q=1/2.
Hence

Final Answer: The probability that exactly 6 insects will survive is 0.2256