A certain insecticide kills 70%
of all insects in laboratory experiments. A sample of 10
insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 3
insects will die? Round your answer to four decimal places
To find the probability that exactly 3 insects will die, we can use the binomial probability formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where:
n = total number of trials (10 insects)
k = number of successes (3 insects dying)
p = probability of success on a single trial (0.70)
Plugging in the values:
P(X=3) = (10 choose 3) * 0.70^3 * (1-0.70)^(10-3)
P(X=3) = 120 * 0.343 * 0.027
P(X=3) = 1.224
Rounded to four decimal places, the probability that exactly 3 insects will die is 0.1224.