Question

g Use the information below for questions 1 through 5. A San Francisco-based tech firm is able to keep 80% of its new employees after one year. Assume that the retention probability of each new employee is independent of other employees. Q1. What is the chance that two randomly sampled new employees will both be able to survive their first year

Answer 1

0.64 = 64% probability that two randomly sampled new employees will both be able to survive their first year

Explanation:

For each employee, there are only two possible outcomes. Either they survive the first year, or they do not. The probability of an employee surviving the first year is independent of other employees. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

A San Francisco-based tech firm is able to keep 80% of its new employees after one year.

This means that
`p = 0.8`

Q1. What is the chance that two randomly sampled new employees will both be able to survive their first year

This is P(X = 2) when n = 2. So

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 2) = C_(2,2).(0.8)^(2).(0.2)^(0) = 0.64`

0.64 = 64% probability that two randomly sampled new employees will both be able to survive their first year