PROBABILITY AND STATISTICS
Do in notebook in organized manner.
1. A manufacturer has two machines. Machine 1 is slower but more reliable. It produces 25% of
the items with 1% defects. Machine 2 produces the remainder with 3% defects. An item from
the production line is selected at random.
a) Make a tree diagram
b) List the sample space.
c) Find the probability of a defective item
d) Find the probability of a non-defective item
e) Suppose the item is defective. Find the probability it came from machine 1.
2. Place the probabilities on the tree
P(A) = 1/5, P(C|A) = 2/7, P(D|B) = 1/4
Then find the following:
a) P(B)
A
b) P(C)
f) P(A∩B)
c) P(D)
d)P(A|C)
B
e) P(B|D)
g) Are A & B mutually exclusive?
C
D
C
D
h) Are A & B complementary?
3. If P(A) = 4/7 ; P(B)= 2/7
a) If A & B are independent then P(A∩B) = ?
P(AUB)=?
b) If A & B are mutually exclusive the P(A∩B)= ?
P (AUB)= ?
4. If P(A|B)= 0.5 and P(A∩B)= 0.2, find P(B).
5. If P(A|B)= 0.7 and P(B)= 0.8, Find P(A∩B).
6. If P(A) =0.5 , P(B) = 0.4 , and P(A∩B)=0.3, find P(AUB).
7. If P(A)=0.8, P(B)= 0.5, and P(AUB) = 0.9, find P(A∩B).
8. If P(A)= 0.7, P(A∩B)= 0.2, and P(AUB) = 0.8, find P(B).
9. If P(A) 4/16, P(B) = 5/16, and P(AUB) = 10/16, find P(A∩B).
10. An urn contains 6 red, 5 blue, 12 green, 3 yellow, and 2 white marbles. Find
a) P(G)
b) P(B|𝐺̅ )
̅̅̅̅̅̅ )
c) P(R|𝐵𝑈𝐺
11. 6 cards are placed face down on a table. Ace, King, Queen of hearts, Ace, King of diamonds,
and King of clubs.
a) P(K)
b) P(H)
c) P(A|H)
d) P(H|K)
Probability worksheet
1. Assume that 80% of the drivers are rated as “good” and 20% are rated as “poor”. Suppose
that 3% of all “good” drivers receive a ticket and 15% of all “poor” drivers receive a ticket.
What is the probability that a driver is “good”, given that he received a traffic ticket?
2. Suppose that a certain disease can be detected by a laboratory blood test with probability 0.94
(that is, if a person has the disease, the probability 0.94 that the test will reveal it.)
Unfortunately, this test also gives a “false positive” in 1% of the healthy people tested (that is,
if a healthy person takes the test, it will imply [falsely] that he has the disease with
probability 0.01). Suppose that 1000 persons are tested, of whom only 5 have the disease. If
one of the 1000 were selected at random, find that probability that :
A) He is healthy
B) The test shows “positive”
C) He is healthy, given that the test is “positive.”