Download 6.3 Notes

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.
If events A and B are not
disjoint, 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
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.

1)
2)
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.
What is the conditional probability that the household
selected is prosperous given that it is educated?
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 purchases
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?