. A statistical experiment has ten equally likely
outcomes that are denoted by 1, 2, 3, 4,...
. A statistical experiment has ten equally likely
outcomes that are denoted by 1, 2, 3, 4, 5, 6, 7, 8, 9, and
10. Let event A = {3, 4, 6, 9} and event B = {1, 2, 5}.
Use probabilities to answer the following questions
Are events A and B mutually exclusive?
Are events A and B independent?
What are the complements of events A and B and their
probabilities?
1. A random experiment consists of throwing a pair of dice, say
a red die and...
1. A random experiment consists of throwing a pair of dice, say
a red die and a green die, simultaneously. They are standard
6-sided dice with one to six dots on different faces. Describe the
sample space.
2. For the same experiment, let E be the event that the sum of
the numbers of spots on the two dice is an odd number. Write E as a
subset of the sample space, i.e., list the outcomes in E.
3. List...
Suppose that we have a sample space with six equally likely
experimental outcomes: x1, x2, x3,...
Suppose that we have a sample space with six equally likely
experimental outcomes: x1, x2, x3, x4, x5, x6, and that A = { x2,
x3, x5} and B = { x1, x2} and C= {x1, x4, x6}, then P(A ∩
B) =
A probability experiment is conducted in which the sample space
of the experiment is S={7,8,9,10,11,12,13,14,15,16,17,18}, event...
A probability experiment is conducted in which the sample space
of the experiment is S={7,8,9,10,11,12,13,14,15,16,17,18}, event
F={7,8,9,10,11,12}, and event G={11,12,13,14}. Assume that each
outcome is equally likely. List the outcomes in F or G. Find P(F or
G) by counting the number of outcomes in F or G. Determine P(F or
G) using the general addition rule.
in an experiment , two dice are tossed , all outcomes are
equally likely . Let...
in an experiment , two dice are tossed , all outcomes are
equally likely . Let X the RV such that X is the product of the two
numbers of the dots shown .
a) Find the sample space of X.
b) Find pmf of X .
Suppose that we have a sample space with five equally likely
experimental outcomes: E1, E2, E3,...
Suppose that we have a sample space with five equally likely
experimental outcomes: E1, E2, E3, E4, E5. let
a = {E1, E2}
B = {E3, E4}
C = {E2, E3, E5}
a. Find P(a), P(B), and P(C).
b. Find P(a ∙ B). Are a and B mutually exclusive?
c. Find ac, Cc, P(ac), and P(Cc).
d. Finda∙Bc andP(a∙Bc).
e. Find P(B ∙ C ).