Question

Assume you have a group of ten ping-pong balls numbered from 1-10. Let us define some events as follows:
	Event A: A randomly selected ball has an odd number on it
	Event B: A randomly selected ball has a multiple of 3 on it
	Event C: A randomly selected ball has either a 5 or 8 on it
Answer the following questions related to probability of the above described events for a SINGLE trial:
a.	P(A) =	(Remember this is asking,"What is the probability that a randomly selected ball meets Event A's description?")
b.	P(B) =
c.	P(A and C) =
d.	P(A or C) =
e.	P(not A) =
f.	P(B given A) =
g.	Describe the complement of Event B.
h.	From the 3 events listed above (Events A, B, & C), is any pair mutually exclusive? Explain your answer.

Answer 1

A consists of {1,3,5,7,9}

B consists of {3,6,9}

C consists of {5,8}

(a) P(A) = 5/10 = 0.5

(b) P(B) = 3/10 = 0.3

(c) P(A and C) = P{5} = 1/10 = 0.1

(d) P(A or C) = P{1,3,5,7,8,9} = 6/10 = 0.6

(e) P(not A) = 1 - P(A) = 0.5

(f) P(B given A) = P(B and A)/P(A)

= P{3,9}/0.5 = 0.2/0.5 = 0.4

(g)The complement of event B, B' is the event that a randomly selected ball has a number which is not a multiple of 3

B' consists of {1,2,4,5,7,8,10}

(h) Events B and C are mutually exclusive as they do not have any element in common i.e B intersection C is a null set