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- Problems on conditional probability
Given the following data:
Determine, if possible, the conditional probability
.
% file
npr03_01.m % Data for
[link] minvec3
DV = [A|Ac; A; A&B; B&C; Ac|(B&C); Ac&B&Cc];DP = [ 1 0.55 0.30 0.20 0.55 0.15 ];TV = [Ac&B; B];disp('Call for mincalc')
npr03_01Variables are A, B, C, Ac, Bc, Cc
They may be renamed, if desired.Call for mincalc
mincalcData vectors are linearly independent
Computable target probabilities1.0000 0.2500
2.0000 0.5500The number of minterms is 8
The number of available minterms is 4- - - - - - - - - - - -
P = 0.25/0.55P = 0.4545 Got questions? Get instant answers now!
In
Exercise 11 from "Problems on Minterm Analysis," we have the following data:
A survey of a represenative group of students yields the following information:
- 52 percent are male
- 85 percent live on campus
- 78 percent are male or are active in intramural sports (or both)
- 30 percent live on campus but are not active in sports
- 32 percent are male, live on campus, and are active in sports
- 8 percent are male and live off campus
- 17 percent are male students inactive in sports
Let A = male, B = on campus, C = active in sports.
- (a) A student is selected at random. He is male and lives on campus. What is
the (conditional) probability that he is active in sports?
- (b) A student selected is active in sports. What is the(conditional) probability
that she is a female who lives on campus?
npr02_11 - - - - - - - - - - - -
mincalc- - - - - - - - - - - -
mincalctEnter matrix of target Boolean combinations [A&B&C; A&B; Ac&B&C; C]
Computable target probabilities1.0000 0.3200
2.0000 0.44003.0000 0.2300
4.0000 0.6100PC_AB = 0.32/0.44
PC_AB = 0.7273PAcB_C = 0.23/0.61
PAcB_C = 0.3770 Got questions? Get instant answers now!
In a certain population, the probability a woman lives to at least
seventy years is 0.70 and is 0.55 that she will live to at least eighty years.If a woman is seventy years old, what is the conditional probability she will
survive to eighty years?
Note that if
then
.
Let
event she lives to seventy and
event she lives to eighty.
Since
,
.
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From 100 cards numbered 00, 01, 02,
, 99, one card is drawn.
Suppose
A
i is the event the sum of the two digits on a card is
and
B
j is the event the product of the two digits is
j . Determine
for each possible
i .
B
0 is the event one of the first ten is drawn.
is the event
that the card with numbers
is drawn.
for
each
i , 0 through 9.
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Two fair dice are rolled.
- What is the (conditional) probability that one turns up two spots, given
they show different numbers?
- What is the (conditional) probability that the first turns up six, given that
the sum is
k , for each
k from two through 12?
- What is the (conditional) probability that at least one turns up six, given that
the sum is
k , for each
k from two through 12?
- There are
ways to choose all different. There are
ways that they are different and one turns up two spots. The conditional probability is
2/6.
- Let
event first is a six and
event the sum is
k . Now
for
. A table of sums shows
and
for
through 12, respectively.
Hence
, respectively.
- If
is the event at least one is a six, then
for
through 11 and
. Thus, the conditional
probabilities are 2/6, 2/5, 2/4, 2/3, 1, 1, respectively.
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Source:
OpenStax, Applied probability. OpenStax CNX. Aug 31, 2009 Download for free at http://cnx.org/content/col10708/1.6
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