Answer: 0.2401
Step-by-step explanation:
The binomial distribution formula is given by :-
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex]
where P(x) is the probability of x successes out of n trials, p is the probability of success on a particular trial.
Given : The probability that a randomly chosen citizen-entity of Cygnus is of pension age† is approximately: p =0.7.
Number of trials : n= 4
Now, the required probability will be :
[tex]P(x=4)=^4C_4(0.7)^4(1-0.7)^{4-4}\\\\=(1)(0.7)^4(1)=0.2401[/tex]
Thus, the probability that, in a randomly selected sample of four citizen-entities, all of them are of pension age =0.2401
