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Birthday Problem
• The probability of 2 people having the same birthday
in a room of 41 people is 90%.
• To randomly select ___ birthdays, randInt (1, 365,
__)L1:SortA(L1)
This will sort the day in increasing order; scroll
through the list to see duplicate birthdays. Repeat
many times.
• The following short program can be used to find the
probability of at least 2 people in a group of n people
having the same birthday
: Prompt N
: 1- (prod((seq((366-X)/365, X, 1, N, 1))
A couple plans to have three children.
Find the probability that the children are:
(a) all boys
(b) all girls
(c) exactly two boys or exactly two girls
(d) at least one child of each sex
The union of a collection of events:
The Additional Rule of Disjoint Events:
General Addition Rule for Unions of 2 Events:
• If events A and B are
_________________,
they can occur
simultaneously.
• Outcomes in common!
In a statistics class there are 18 juniors and
10 seniors; 6 of the seniors are females, and
12 of the juniors are males. If a student is
selected at random, find the probability of
selecting
(a) a junior or a female
(b) a senior or a female
(c) not a junior male
Example 6.23, p. 438
• Deborah guesses that the prob.
of making partner in the firm is
0.7 and that Matthew’s is 0.5.
She guesses that the prob. that
both make partner is 0.3.
1) Find P(at least one is made
partner)
2) P(neither is made partner)
3) P(Deborah makes partner and
Matthew does not)
3) P(Matthew makes partner and
Deborah does not).
• Let A = the woman
chosen is 18-29
• Let B = the woman
is married
Find:
1) P(A)
2) P(A and B)
3) P(B given A)
• The probability we assign to an event if we
know that some other event has occurred.
Call a household prosperous if its income exceeds
$100,000. Call the household educated if the
householder completed college. Select an American
household at random, and let A be the event that the
selected household is prosperous and B the event
that it is educated. According to the Current
Population Survey, P(A) = 0.138, P(B) = 0.261, and
the probability that a household is both prosperous
and educated is P(A and B) = 0.082.
1) What is the conditional probability that the household
selected is prosperous given that it is educated?
2) Are A and B independent? Use both methods of
determining whether or not two events are
independent.
• Seventy-five percent of people who purchase hair dryers are
women. Of these women purchases of hair dryers, thirty
percent are over 50 years old. What is the probability that a
randomly selected hair dryer purchaser is a woman over 50
years old?
• An insurance agent knows that 70 percent of her customers
carry adequate collision coverage. She also knows that of
those who carry adequate coverage, 5 percent have been
involved in accidents and of those who do not carry adequate
coverage, 12 percent have been involved in accidents. If one
of her clients gets involved in an accident, then what is the
probability that the client does not have adequate coverage?
70% of people buy Brand 1 DVD player. 30% buy
Brand 2. Of those who buy a DVD player, 20% of
those who buy Brand 1 also get the extended
warranty and 40% of those who buy Brand 2 get it.
Make a tree diagram and then find the following:
1) What is the probability that they got Brand 1 and the
extended warranty?
2) What is the probability that they got Brand 2 and no
extended warranty?
3) What is the probability that they bought brand 2 if
they got the extended warranty?
4) What is the probability they bought Brand 1 if they
didn’t get the extended warranty?