Question

The probability that a randomly chosen citizen-entity of Cygnus is of pension age† is approximately 0.7. What is the probability that, in a randomly selected sample of four citizen-entities, all of them are of pension age?

Answer 1

Answer: 0.2401

Explanation:

The binomial distribution formula is given by :-

`P(x)=^nC_xp^x(1-p)^(n-x)`

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 :

`P(x=4)=^4C_4(0.7)^4(1-0.7)^(4-4)\\\\=(1)(0.7)^4(1)=0.2401`

Thus, the probability that, in a randomly selected sample of four citizen-entities, all of them are of pension age =0.2401