statistics

1. (7 points) The following is known. 2% of women have breast cancer. 80% of
mammograms detect breast cancer when it is there (and therefore 20% miss it).
9.6% of mammograms detect breast cancer when its not there (and therefore
90.4% correctly return a negative result).

a) A woman was picked randomly was given a mammogram test. What is the
probability that she will be tested positive?

b) Suppose she was tested positive. What is the probability that she actually
has breast cancer?

2. (7 points) A shipment of 25 items contained 5 defectives. The buyer tested 7
randomly selected items from the lot.

a) What is the probability that she will find exact two defectives in the sample?
b) What is the probabilility that she will find at least one defective in the
sample?

3.183 Series and parallel systems. Consider the two systems
shown in the schematic on page 174. System A operates
properly only if all three components operate properly.
(The three components are said to operate in series.) The
probability of failure for system A components 1, 2, and 3 is
12, .09, and .11, respectively. Assume that the components
operate independently of each other.
174 CHAPTER 3 Probability
System A: Three Components in Series
Input ->.-‘.-.-’ Output
System B: Two Parallel Subsystems
o Subsystem C Q
Input -< -* Output
Subsystem D

System B comprises two subsystems said to operate in a. It is known that the proportions
parallel. Each subsystem has two components that operate produced by the seven supplie
in series. System B will operate properly as long as at least .006, .0002, .0002, and .001, resp
one of the subsystems functions properly. The probability microchip failure is observed,
of failure for each component in the system is .1. Assume likely responsible?
that the components operate independently of each other. b. Suppose the seven suppliers pr
a. Find the probability that System A operates chips at the same rate, 9005, If

P1“ OPCT lY- failure is observed, which suppli-
b. What is the probability that at least one of the compo- sible?

t’ St Awillf’l dth f thtth t

3 fsalilllq ys em a1 an ere ore a e sys em *3.186 Dream experiment in psycholog
c. Find the probability that System B operates properly. ‘3 glst ls grvg: tapes if 120 $113)]?th
(1. Find the probability that exactly one subsystem in reams. . .e . psyc 0 ong ls 0

System B fails anx1ety 1nd1v1duals and 10 are 10
e. Find the probability that System B fails to operate Elijfcsgmdogm S task 1s to sele

properly.
f. How many parallel subsystems like the two shown here 3’ Count the number of sample

would be required to guarantee that the system would ment.

operate properly at least 99% of the time? b- Assuming that the PSYChOIOEISt