Statistics and Probability Answers

The probability that a student pilot passes the
written test for a private pilot’s license is 0.7. Find the
probability that a given student will pass the test
(a) on the third try;
(b) before the fourth try.

A box contains 4 red and 5 blue marbles. Michele picks three marbles at random from this box. If Z is a random variable representing the # of blue marbles picked from the box, do the following:
a. Express the probability mass function of Z in tabular form.
b. Draw the corresponding histogram.
c. Compute the probability that Michele can pick more red marbles than blue from the box.

Suppose that airplane engines operate independently
and fail with probability equal to 0.4. Assuming
that a plane makes a safe flight if at least one-half of its
engines run, determine whether a 4-engine plane or a 2-
engine plane has the higher probability for a successful
flight.

A nationwide survey of college seniors by the
University of Michigan revealed that almost 70% disapprove
of daily pot smoking, according to a report in
Parade. If 12 seniors are selected at random and asked
their opinion, find the probability that the number who
disapprove of smoking pot daily is
(a) anywhere from 7 to 9;
(b) at most 5;
(c) not less than 8.

According to a study published by a group of University
of Massachusetts sociologists, approximately
60% of the Valium users in the state of Massachusetts
first took Valium for psychological problems. Find the
probability that among the next 8 users from this state
who are interviewed,
(a) exactly 3 began taking Valium for psychological
problems;
(b) at least 5 began taking Valium for problems that
were not psychological

It is known that 60% of mice inoculated with a
serum are protected from a certain disease. If 5 mice
are inoculated, find the probability that
(a) none contracts the disease;
(b) fewer than 2 contract the disease;
(c) more than 3 contract the disease.

A nationwide survey of 17,000 college seniors by
the University of Michigan revealed that almost 70%
disapprove of daily pot smoking. If 18 of these seniors
are selected at random and asked their opinion, what
is the probability that more than 9 but fewer than 14
disapprove of smoking pot daily?

A random committee of size 3 is selected from
4 doctors and 2 nurses. Write a formula for the probability
distribution of the random variable X representing
the number of doctors on the committee. Find
P(2 ≤ X ≤ 3).

A company is interested in evaluating its current
inspection procedure for shipments of 50 identical
items. The procedure is to take a sample of 5 and
pass the shipment if no more than 2 are found to be
defective. What proportion of shipments with 20% defectives
will be accepted?

Find the probability of being dealt a bridge hand
of 13 cards containing 5 spades, 2 hearts, 3 diamonds,
and 3 clubs.