To find the probability that less than 5 insects will die out of 12 exposed to the insecticide, we can use the binomial probability formula.
The formula for the probability of getting exactly k
successes in n
trials, where the probability of success in a single trial is P , Is given by:
P（X=k）=（xpx（1-p）コーん
Given that the insecticide kills 60% of insects in experiments, the probability of an insect dying in a single trial (P ) is 0.6, and the probability of an insect
surviving in a single trial is 1 - p = 0.4
Now, we need to find the probability that less than 5 insects will die. We calculate this by finding the individual probabilities of 0, 1, 2, 3, and 4 insects dying and then summing them up.
P(X < 5) = P(X = 0) + P(X = 1) + Р(Х =
Calculating each probability:
- For k = 0
P（X=0）=（3）x0.60x0.422
- For k = 1
, P(X = 1) = (13) × 0.61 × 0.411
- For k = 2
, P(X = 2) = (2) × 0.62 × 0.410
- For k = 3
，P×=3=（×0.68×0.49
- For k = 4
, P(X = 4) = (1) × 0.64 × 0.48
Summing these individual probabilities will give us the probability that less than 5 insects will die when 12 are exposed to the insecticide.
