Q1 out of 5 Mathematicians and 7 physicists, a committee
consisting of 2 mathematicians and 3 physicists is to be formed. In how
many ways can this be done if any mathematician and any physicist can be
included?
Q2 Two petrol
station are located in a street at Victoria island, each of the petrol
station has 5 pumps, an experiment was carry out to determine the number
of pumps in use at a particular time of the day at each of the petrol
station, assume an experimental outcome is (x,y), where x specified the
number of pumps in use at the 1st station and y the number of pumps in
use at the second station. How many of such outcome will you have in
this experiment?
Q3 Evaluate (x-2)!(y-4) if x=6 and y=9
Q4 Set X has 8 elements and set Y has 10 elements, if there are 5
common elements in X and Y, what is the cardinality of X union Y?.
Q5 In how many way can 6 people take place at a round table?
Q6 how many 3 digits numbers greater than 300 can be formed using the
digits 1, 2, 3, 4, 5 if no digit can be repeated and the first digit
cannot be 3?
Q7 A bus
starts with 6 people and stops at 10 different stops. how many different
ways can the 6 people depart if any passenger can depart at any bus
stop
Q8 How many runs of L do your have in the following sequences WWWWWLLWLWWLLWWW
Q9 Among the 120 applicants for a job, only 80 are actually qualified.
If five of the applicants are randomly selected for an in- depth
interview, find the probability that only two of the five will be
qualified for the job (answer to 3 decimal places)
Q10 in a given business venture a lady can make a profit of N300 with
probability 0.6 or take a loss of N100 with probability 0.4. what is her
expectation?N
Q11 if a
man purchases a rafle ticket, he can win a first prize of N5000 or a
second prize of N2000 with probabilities 0.001 and 0.003. what should be
a fair price to pay for the ticket? N
Q12 Find the probability that a random variable having the standard
normal distribution will take on a value less than -0.88 (answer to 4
decimal places)
Q13 If X has the probability density $$f(x)=k.e^{-3x} $$ for x>0, find the value of k
Q14 Which law states that $$(A\cap B)^{c}=A^{c}\cup B^{c}$$? It is Law
Q15 When P(AnB) = P(A) . P(B), events A and B are said to be
Q16 A certain shop repairs both audio and video components. Let A
denote the event that the next component brought in for repair is an
audio component, and let B be the event that the next component is a
compact disc player (so the event B is contained in A). Suppose that
P(A)= 0.6 and P(B) =0.05. What is P(P|A)?
Q17 When you toss 5 coins once, if the number of
head(s) is the random variable define on the resulting sample space.
What is the set of random variable resulting from this experiment?
Q18 A ____________________ random variable is memoryless
Q19 If x is a normal variable with the mean u=5 and
variance (sigma square)=16, what is the probability that x is less than
or equal to 6?
Q20 Let X have a standard gamma distribution with alpha =7. Compute P(X <4 or X>6)
Q21 Let X have a uniform distribution on the interval [A,B]. compute V(X)
Q22 In a study of plants, five characteristics are to
be examined. If there are six recognizable differences in each of four
characteristics and eight, recognizable difference in the remaining
characteristics. How many plants can be distinguished by these five
characteristics?
Q23 A student is to answer all the nine questions in
an examination. It is believed that the sequence in which the questions
are answered may have a considerable effect on the performance of the
student. In how many different order can the question be answered
Q24 A coin is rolled thrice, what is the probability for an event that at least two head or at least two tails occurs?
Q25 The 3rd and 7th term of a G.P. are 81 and16 respectively, find the 1st and 5th term
Q26 For a sequence 128, 64, 32, ……………………….. what is the value 12th term of this sequence?
Q27 Given two set A={5,6,7,8,9,10} and B={x:5 <x <10}. Find A/B
Q28 Suppose a factory has three machines M1, M2, M3
which produce 60%, 30% and 10% of the total production respectively. Of
their output, machine M1 produces 2% defective items, machine M2
produce 3% defective items while machine M3 produces 4% defective items.
Find the probability that a part selected at random is defective.
Q29 Identify the expression for the moment generating function of a poisson random variable
Q30 If the probability is 0.40 that a child exposed
to a certain contagious will catch it, what is the probability that the
tenth child exposed to the disease will be the third to catch it?
Q31 Two fair dies are rolled once. Find the probability that the sum of the numbers on the two faces is greater than Ten
Q32 The rth moment about the origin of the gamma distribution is given by
Q33 For X a continuous random variable with pdf
$$f(x)=\lambda e^{-\lambda x}$$, for x greater than zero and less than
infinity, find the mean of
Q34 Find the expected value of the random variable Y
whose probability density is given by $$f(y)=\frac {1}{8}(y+1)$$ for 2
<y <4
Q35 A random variable having its probability density function given by $$P(x)=\binom{x-1}{r-1}p^{r}(1-p)^{x-r}$$ is called____