solution

The head of human
resources of a company performs a ten-item test on applicants for a position,
taking four possible answers for each item, of which only one is correct.
Assuming the applicants having the same probability of responding. It is asked
to find the probabilities for the applicant:

a)Answer all the
items wrong

b)Answer at least 3
items correctly.

c)Answer between 5
and 7 items well

d)Answer all the
items correctly

e)Answer less than
4 items well

2)On average, five
birds collide with the Washington Monument and die from it each week. Bill
Garcy, an official with the United States National Park Service, has requested
that the US Congress allocate funds to purchase equipment that will keep the
birds away from the monument. A congressional subcommittee has responded that
they cannot allocate funds for this purpose unless the probability of more than
three birds dying each week is greater than 0.7. Should funds be used to scare
birds?

3)The concert pianist
Donna Prima is very upset by the number of coughs that occur in the audience
just before she starts to play. During her last tour, Donna estimated an
average of eight coughs just before starting her concert. Mrs. Prima has warned
her conductor that if she hears more than five coughs at the concert that
night, she will refuse to play. What will be the probability that the artist
will play that night?