Math 30011, Homework #1
#1. Give 3possible sample spaces related to the experiment of tossing a pair of dice.
#2. Let S={1,2,3,4,5,6,7}be a sample space, and events A={1,2,3},B={3,4,5},
C={2,3,7}. Find A∪B,A∪C,A∪B∪C,A∩B,B∩C,A∩B∩C, and Ac.
#3. A pair of fair dice are tossed and the two numbers appearing on the faces are recorded. Let
Ajbe the event “the difference of the two numbers is j”. Find P(Aj)for j= 0,1,5, and 6.
#4. A standard deck of cards contains 52 cards. One card is randomly selected from the deck.
(a). Compute the probability of randomly selecting a heart or club from a deck of cards.
(b). Compute the probability of randomly selecting a two, or three, or four from a deck of cards.
(c). Compute the probability of randomly selecting a two or club from a deck of cards.
#5. In a national survey in order to determine college students’ health-risk behaviors, college
students were asked: “How often do you wear a seat belt when riding in a car driven by someone
else?” The frequencies appear as follows (given as Answer (#of students)): Never (125),
Rarely (324), Sometimes (552), Most of the times (1,257), Always (2,518).
(a). Approximate the probability that a randomly selected college student never or rarely wears
a seat belt when riding in a car driven by someone else.
(b). Approximate the probability that a randomly selected college student does not always wear
a seat belt when riding in a car driven by someone else.
#6. Consider an experiment in which a single card is randomly drawn from a deck. Let Abe the
event “draw a face card”, Bbe the event “draw a club”. Find P(A),P(A|B). Are the events A
and Bindependent?
#7. For the month of June in the city of Chicago, 37% of the days are cloudy, 21% of the days
are cloudy and rainy. What is the probability that a randomly selected day in June will be rainy
if it is cloudy?
#8. Suppose that Aand Bare two events and that P(A)=0.6,P(B)=0.4, and P(A|B)=0.3.
What is the value of P(B|A)?
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