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.
Explanation: The probability of x successes in n trials is:
[tex]_nC_xp^xq^{n-x}[/tex]
Where p and q are the probabilities of success and failure.
Here p=q=1/2.
Hence
[tex]\begin{gathered} P(\text{ exactly 6 will survive\rparen=}_{11}C_6(0.5)^6(0.5)^5 \\ =462\cdot(0.5)^6\cdot(0.5)^5 \\ =0.2256 \end{gathered}[/tex]
Final Answer: The probability that exactly 6 insects will survive is 0.2256
