Question

01:13:53 A certain insecticide kills 70 % of all insects in laboratory experiments. A sample of 7 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 4 insects will survive? Round your answer to four decimal places. AnswerHow to Enter) 1 Point Tables Keypad Keyboard Shortcuts < Next Prev

Answer 1

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%