Answer :
Answer:
7.74%
Step-by-step explanation:
Let X, be the number of insects killed, the probability that exactly 5 insects will survive is the probability of killing exactly two insects.
Probability of success, P(X) = 0.6
Number of successes, X = 2 deaths
Number of trials, n = 7 insects
[tex]P(X=2) = \frac{7!}{(7-2)!2!}*0.6^2*0.4^{7-2}\\ P(X=2) = 0.0774=7.74\%[/tex]
The probability that exactly 5 insects will survive is 7.74%.
Answer:
0.2207
Step-by-step explanation:
P(insect is killed) = 0.6
P(insect survives) = 1 - 0.6 = 0.4
Sample size (n) = 11
X Binomial (p=0.40, n=11)
[tex]P(X=x) = ^nC_{x} * p^x * (1 - p)^{n-x }[/tex]
[tex]P(X=x) = ^{11}C_{x} * 0.40^x * (1 - 0.40)^{11-x}[/tex]
[tex]P(X=x) = ^{11}C_{x} * 0.40^x * 0.60^{11-x}[/tex]
[tex]P(x = 5) = ^{11}C_{5} * 0.40^5 * 0.60^{11-5 }[/tex]
= [tex]^{11}C_{5} * 0.40^5 * 0.60^6[/tex]
= 0.2207 (4 d.p)