Search & Filtering
If P(A) = 0.60, P(B) = 0.30 and P(A and B) = 0.18, then events A and B are?
- independent and mutually exclusive events
- independent but not mutually exclusive events
- dependent but not mutually exclusive events
- dependent and mutually exclusive events
The table below displays results from experiments with polygraph instruments. Find the positive predictive value for the test. That is, find the probability that the subject lied, given that the test yields a positive result.
No_(Did_Not_Lie) Yes_(Lied)
Positive_test_results 14 43
Negative_test_results 34 12
The random variable X has a normal distribution with mean 6.5 and variance 9. Find the value of x, call it
xo, such that P(xo ≤ x ≤ 7) = 0.6853
A person has agreed to participate in an extrasensory perception (ESP) experiment. He is asked to randomly pick two numbers between 1 and 6 (inclusive). In addition, the second number must be different from the first. Let H = event the first number picked is a 3. K = event the second number picked exceeds 4.
(a) Find P(H).
(b) Find P(K|H). Hint: given that the 1st number is 3, what numbers are left for the man to select from? (c) Find P(K & H). Hint: use the multiplication rule. Are these events independent?
(d) Find the probability that both numbers picked is less than 3. Hint: redefine H and K appropriately and follow the same pattern as parts (a)-(c).
From past experience, an oil exploration company knows that each new well drilled has a 32% chance of being viable for oil production. The company is planning to drill five new wells. Assume that all wells are independent.
(a) What is the probability that the first well will not be viable?
(b) What is the probability that none of the five wells will be viable?
(c) What is the probability that at least one of the five wells will be viable?
Suppose you roll two dice, one black, and one red. You record the outcomes in order. For example, the outcome (35) denotes a 3 on the black die and a 5 on the red die. Let A be the event that the black die is even, B be the event that the red die is odd, and C is the event that the dice sum to 10.
(a) (4pts) List or describe the outcomes in the sample space S and the events in A, B, and C. Report the number of outcomes in each set.
(b) (1pt) Find P(A), P(B), and P(C).
(c) (2pts) Find P(A and B). Are A and B independent?
(d) (2pts) Find P(A and C). Are A and C independent?
Lucy is taking English and history. Let E be the event that Lucy gets an A in her English class and let H be the event that she gets an A in her history class. At the beginning of the term these probabilities were P(E) = 0.60 P(H) = .70 P(E and H) = 0.55
(a) Are the events E and H independent? Explain how you know.
(b) Find the probability that Lucy will get at least one A between her English and history classes
Suppose we have a sample of 7445 naturalized US citizens. We have the events given in the table below. Suppose we choose someone from this group at random events.
(a) Find P(A) Event Size
(b) Find P(Ac ) A under 20 2450
(c) Find P(B) B 30 to 64 1850
(d) List all pairs of events that are mutually exclusive. C 50 + 2125
(e) Find P(A or B) D 65 + 1020
Suppose that we randomly select a student and record how many days they worked during the previous week.
(a) Make a list of all the simple events in the sample space.
(b) List the simple events that make up each of the following events:
i. The student worked at least 4 days.
ii. The student worked every day.
Ben is a member of a class with 25 students that meets five days per week. Each day class meets, a student in the class is randomly selected to explain how to solve a homework problem. Once a student has been selected, he or she will not be selected again that week. If Ben was not one of the four students selected earlier in the week, what is the probability that he will be picked on the last day of class during the week?
