# Thread: 3 Quick Probability questions

1. ## 3 Quick Probability questions

1) the secretary of a college has calculated that from the students who took calculus, physics and chemistry last semester:
78% passed calculus
80% passed physics
84% chemistry
60% calculus and physics
65% physics and chemistry
70% calculus and chemistry,
and 55% all three.

Show that these numbers are not consistent, and therefore the secretary has made a mistake

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2) If X is uniformly distributed on {a,b}, find the moment generating function of X
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3) that detects missing pulses. The number of errors found in an eight bit byte is a random variable with the following distribution:

F(x)= 0 if x <1
0.7 if 1<= x <4
0.9 if 4<= x <7
1 if x =>7

find the following:

a. P(X<=4)
b) P(X>7)
c) P(X<=2)

2. Hello, Andreamet!

1) The secretary of a college has calculated that from the students
who took calculus, physics and chemistry last semester:

78% passed calculus
80% passed physics
84% passed chemistry
60% passed calculus and physics
65% passed physics and chemistry
70% passed calculus and chemistry, and
55% passed all three.

Show that these numbers are not consistent,
and therefore the secretary has made a mistake
We have this formula:
. . $n(A\,\cup\,B\,\cup\,C) \;=\;n(A) + n(B) + n(C) - n(A\,\cap\,B)$ $- n(B\,\cap\,C) - n(A\,\cap\,C) + n(A\,\cap\,B\,\cap\,C)$

Then we have:
. . $n(\text{Calc }\cup\text{ Phys } \cup\text{ Chem}) \;=\;78\%\,+\,80\%\,+\,84\%\,-\,60\%\,-\,65\%\,-\,70\%\,+\,55\% \;=\;102\%$

The data adds up to more than 100% . . . clearly impossible.