Question

A certain insecticide kills 50% of all insects and a laboratory experiments. a sample of 11 insects is exposed to the insecticide in a particular experiment what is the probability that exactly 6 insects will survive?round your answer to four decimal places

Answer 1

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:

$_nC_xp^xq^{n-x}$

Where p and q are the probabilities of success and failure.

Here p=q=1/2.

Hence

$\begin{gathered} P(\text{ exactly 6 will survive\rparen=}_{11}C_6(0.5)^6(0.5)^5 \\ =462\cdot(0.5)^6\cdot(0.5)^5 \\ =0.2256 \end{gathered}$

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