Department of Mathematics
MAL 250 (Probability and Stochastic Process)
Tutorial Sheet No. 1
1. Items coming oﬀ a production line are marked defective (D) or nondefective (N). Items are observed and
their condition noted. This is continued until two consecutive defectives are produced or four items have
been checked, which ever occurs ﬁrst. Describe the sample space for this experiment.
2. During a 24hour period, at sometime
X
, a switch is put into “ON” position.Subsequently, at some future
time
Y
(still during that same 24hour period) this switch is put into the “OFF” position. Assume that
X
and
Y
are measured in hours on the time axis with the beginning of the time period as the origin. The
outcome of the experiment consists of the pair of numbers (
X,Y
).
(a) Describe the sample space.
(b) Describe and sketch in the
X

Y
plane the following events
i. The circuit is ON for one hour or less.
ii. The circuit is ON at time
z
, where
z
is some instant during the given 24hours period.
iii. The circuit is turned ON before time
t
1
and turned OFF after time
t
2
, where again
t
1
< t
2
are two
time instants during the speciﬁed period.
iv. The circuit is ON twice as long as it is OFF.
3. The probability that a person stepping at a gas station will ask to have his tires checked is 0.12, the probability
that he will ask to have his oil checked is 0.29, and the probability that he will ask to have both of them
checked is .07. What is the probability that he will get (a) neither of the two checked (b) exactly one of the
two checked?
4. Given
P
(
A
) =
.
35,
P
(
B
) =
.
73 and
P
(
A
∩
B
) =
.
14. Find
P
(
¯
A
∩
¯
B
),
P
(
A
∪
¯
B
),
P
(
¯
A
∪
B
).
5. Consider a randomly chosen group of
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 Spring '11
 rsharma
 Probability, Probability theory, 24hour, 30%, 24hours

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