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a) A business receives order at an average rate of 1 per minute.What is the probability of getting three orders in one minute?
b) An emergency service receives an average of 2.1 false alarms per day.What is the probability of getting four false alarms in a given day?
c) On average the demand for a certain product is four per week.If the stock at the beginning of each week is renewed so that there are always 6 in store , What is the probability of running out of stock in any week.
d) A call center has a capacity to deal with 25 calls per minute on average.what is the probability of getting 30 calls in any minute period?
e) The average time taken for a worker to assemble a certain product is 45 minutes.There are 10 workers employed to make these assemblies.What is the probability of assembling 10 units in an hour?
Let X be a random variable . P(X=-2)=P(X=-1),P(X=2)=P(X=1),P(X=0)=P(X>0)=P(X<0) . obtain the probability mass function of X.
Research has shown that 55% of new Small Medium Enterprises (SMEs) are started by graduates
while 45% are started by non-graduates. It is also known that 70% of SMEs started by graduates are
successful i.e. they survive beyond 3 years, while only 10% of those started by non-graduates are
successful.
9. A large company that must hire a new president prepares a final list of five candidates, all
of whom are qualified. Two of these candidates are members of a minority group. To
avoid bias in the selection of the candidate, the company decides to select the president
by lottery. What is the probability that one of the minority candidates is hired?
10. On February 1, 2003, the space shuttle Columbia exploded. This was the second disaster
in 113 space missions for NASA. On the basis of this information, what is the probability
that a future mission is successfully completed?
11. What is the probability that a card chosen at random from a standard deck of cars will be
either a king or a heart?
12. In testing a certain kind of truck tire over rugged terrain, it is found that 25% of the trucks
fail to complete the test run without a blowout. Of the next 15 trucks tested, find the
probability that
(a) from 3 to 6 have blowouts;
(b) fewer than 4 have blowouts;
(c) more than 5 have blowouts
Two ordinary six-sided dice were tossed. Set up a sample space for this experiment and
hence find the probability that
i. Sum of the points on the two dice is 7,
ii. Points on the first die are greater than the points on the second die,
iii. First die shows an even number,
6. Two ordinary six-sided dice were tossed. Set up a sample space for this experiment and
hence find the probability that
i. Sum of the points on the two dice is 7,
ii. Points on the first die are greater than the points on the second die,
iii. First die shows an even number,
iv. Points on the dice are the same, (i.e. throwing a double),
v. Difference in the outcomes of two dice is 2.
7. Suppose that two machines I and II in a factory operate independently of each other. Past
experience showed that during a given 8-hour time, machine I remains inoperative one
third of the time and machine II does so about one fourth of the time. What is the
probability that at least one of the machines will become inoperative during the given
period?
8. Two coins are tossed. If A is the event “head on the first coin”, B is the event “head on
the second coin” and C is the event “coins fall alike”, show that the events A, B, and C
are pair wise independent but not completely independent.
A magazine reported that 6% of American drivers read the newspaper while driving. If 300 drivers are selected at random, find the probability that exactly 25 say they read the Newspaper while driving.
1. A card is drawn at random from an ordinary pack of 52 playing cards. Find the probability that the card is a seven.
2. An ordinary die is rolled once. Find the probability that
i. An even number occurs
ii. A number greater than 4 occurs
3. Examination results of 150 students showed that 95 students passed mathematics, 75
students passed economics and 135 students passed at least one of the above subjects. A
student is selected at random. What is the probability that the student
i. Passed both mathematics and economics?
ii. Failed both the subjects?
4. Three horses A, B, and C are in a race. A is twice as likely to win as B, and B is twice as
likely to win as C. What are their respective chances of winning?
5. The probability that a student passes history is 2/3 and that he passes economics is 4/9. If
the probability of passing at least one course is 4/5, what is the probability that he will
pass both courses?
Suppose that two machines I and II in a factory operate independently of each other. Past experience showed that during a given 8-hour time, machine I remains inoperative one third of the time and machine II does so about one fourth of the time. What is the probability that at least one of the machines will become inoperative during the given period
11) To investigate how often family members eat at home, Maya Interactive surveyed 500 adults living with children under the age of 18. The survey results are shown in the following table.
Number of Family Meals per Week - 0,1,2,3,4,5,6,7 or more.
Number of Survey Responses - 20,30,40,112,66,52,56,124.
For a randomly selected family with children under the age of 18, compute the following.
a) The probability of the family eats no meals at home during the week.
b) The probability of the family eats at least five meals at home during the week.
c) The probability of the family eats three or fewer meals at home during the week.
