Independent Probability

$3\mathrm{.}1[1$ pt$]$ The summer youth employment program has $1390$ participants and there are $1105$ jobs available. Suppose that the average number of applications per youth was $1\mathrm{.}8$ and that each youth applies to each job with some constant probability prob$\_$apply. What prob$\_$apply would make an individual youth's expected number of applications equal to $1\mathrm{.}8?$ Hint: Use the result about the expected value of a binomial random variable.

In $[]$: prob$\_$apply $=$ None

# YOUR CODE HERE

raise NotImplementedError$()$

In $[]$: #hidden tests for problem $3\mathrm{.}1$ are within this cell

$3\mathrm{.}2[1$ pt$]$ Consider one individual job. Use scipy's binom.pmf function and your answer for prob$\_$apply to determine the probability that it receives zero applications? Store you answer in the variable prob$\_$zero$\_$applications as a float or numpy float. You will need the correct value for prob$\_$apply in order to find the correct value for prob$\_$zero$\_$applications.

In $[]$: prob$\_$zero$\_$applications $=$ None

# YOUR CODE HERE

raise NotImplementedError$()$

In $[]$:

#hidden tests for problem $3\mathrm{.}2$ are within this cell