There are only two outcomes, i.e, either the insects will survive or they do not. | |||||||
Hence, binomial distribution can be used. | |||||||
The formula to be used is:- | |||||||
P(X) = nCx * px * qn-x | |||||||
Where, | |||||||
P(X) = Probability of x outcomes | |||||||
n= number of samples or trials | |||||||
p = probability of success | |||||||
q = probability of failure | |||||||
Here, | |||||||
n = 7 (there are 7 insects) | |||||||
x = 4 (exactly 4 should survive) | |||||||
p = q = 0.5 (since the probability of survival and not surviving is equal) | |||||||
nCx = | n! | ||||||
x! (n-x)! | |||||||
7c4 = | 7! | = 35 | |||||
4! (7-4)! | |||||||
P(X = 4) = | 7C4 * p4 * q7-4 | ||||||
= | 35 * 0.54 * 0.53 | ||||||
= | 0.273438 | ||||||
= | 27.34% | ||||||
Therefore, the probability that exactly 4 insects will survive = 27.34% |
01:13:53 A certain insecticide kills 70 % of all insects in laboratory experiments. A sample of...
A certain insecticide kills 70% of all insects in laboratory experiments. A sample of 14 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 3 insects will survive? Round your answer to four decimal places.
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