Question

Evans Electronics is concerned about a low retention rate for its employees. In recent years, management has seen a turnover of 10% of the hourly employees annually. Thus, for any hourly employee chosen at random, management estimates a probability of 0.1 that the person will not be with the company next year. Choosing 3 hourly employees at random, what is the probability that 1 of them will leave the company this year?

Answer 1

Answer: 0.243

Step-by-step explanation:

Binomial probability distribution formula :-

$P(X=x)= ^nC_xp^x(1-p)^{n-x}$

As per given we have,

Probability that  the person will not be with the company next year : p=0.1

Sample size = n= 3

Let x be a binomial variable that represents the number of employees  will not be with the company next year.

Then, the probability that 1 of them will leave the company this year :-

$P(X=1)= ^3C_1(0.1)^1(0.9)^{3-1}\\\\=(3)(0.1)(0.9)^2\ \ [\because ^nC_1=n]\\\\=0.243$

Hence, the probability that 1 of them will leave the company this year =0.243