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Answer the following questions:
Four different white flowers, 3 red and 2 yellow are arranged on the table in a line. How many different arrangement are possible if
1-The flowers arranged in any order
(a) 282240 (b) 30240 (c) 1260 (d) 362880 (e) none of these
2- Flowers of the same color are identical
(a) 282240 (b) 30240 (c) 1260 (d) 362880 (e) none of these
3- Only red flowers must be together
(a) 282240 (b) 30240 (c) 1260 (d) 362880 (e) none of these
4-Two particular flowers must not be together
(a) 282240 (b) 30240 (c) 1260 (d) 362880 (e) none of these
In a certain university engage in various sections in the following proportions :
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Civil section 35% of the student, military section 15% of the student and industrial section 25% of the student.
6% of the student study in civil and military sections
7% of the student study in civil and industrial sections
5% of the student study in industrial and military sections
3% of the student study in all sections.
If a student chosen for the interview, calculate the chance that he study
5- In at least one section
(a) 0.35 (b) 0.17 (c) 0.44 (d) 0.6 (e) none of these
6- In military or civil section
(a) 0.35 (b) 0.17 (c) 0.44 (d) 0.6 (e) none of these
7- How many four digit number can be formed if the first number is odd and the last is number 3, if the number can be used only once
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(a) 280 (b) 224 (c) 500 (d) 60 (e) none of these
8- Find the constant term in the expansion EMBED Equation.3
(a) -17920 (b) -70 (c) 256 (d) 17920 (e) none of these
In how many five pharmacist and five doctors be seated in alternate way
9- at a rounded table
(a) 14400 (b) 2880 (c) 28800 (d) 576 (e) none of these
10- in a row
(a) 14400 (b) 2880 (c) 28800 (d) 576 (e) none of these
* Suppose we have a fuse box containing 20 fuses of which 6 are defective .If 3 fuses are selected at random and removed from the box in succession with replacement (('D**'(9 E9 'D%9'/)) ,
11- The probability that three fuses are defective is
(a) 0.027 (b) 0.0175 (c) 120 (d) 0.015 (e) none of these
Consider the experiment of flipping a balanced coin three times independently, then
12- The probability of getting at most two head is
(a) 0.50 (b) 0.375 (c) 0.75 (d) 0.875 (e) none of these
13- The probability of getting exactly one head is
(a) 0.50 (b) 0.375 (c) 0.75 (d) 0.875 (e) none of these
14- The events "The first flip is a head" and "The second and third flip are tail" are
(a) Disjoint (b) independent (c) equally likely (d) none of these
The probability that a computer system has electrical failure is 0.15, and the probability that it has virus is 0.25 and the probability that it has at least one problem is 0.35, then
15- The probability that the computer system has the electrical failure or has no virus is
(a) 0.2 (b) 0.80 (c) 0.0589 (d) 0.2353 (e) none of these
16- If the computer system doesn't has electrical failure, then the probability that it has virus is
(a) 0.2 (b) 0.80 (c) 0.133 (d) 0.2353 (e) none of these
17- A box contain 7 balls colored in different colors, the number of ways that 2 balls are selected without replacement is
(a) 21 (b) 42 (c) 14 (d) 5040 (e) none of these
18- Consider the system of components connected as in the following diagram. If components work independently of one another ,what probability that the system will work ?Let P(A)=0.9,P(B)=0.85,P(C)=0.99,P(D)=0.91
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(a) 0.8872 (b) 0.8178 (c) 0.8987 (d) 0.9985 (e) none of these
Three machines A, B, C of equal capacities are producing kitchen tools. The probability that the machines produce defective kitchen tools that do not satisfy the specifications are 0.1, 0.2 and 0.1 respectively. A kitchen tools is taken at random from a day's production and found to be defective, then
19- The probability that the defective kitchen tools came from machine A is
(a) 0.50 (b) 0.25 (c) 0.133 (d) 0.4 (e) none of these
20- The probability that the defective kitchen tools came from machine A or C is
(a) 0.50 (b) 0.25 (c) 0.133 (d) 0.4 (e) none of these
Let X be uniform distribution with values 5,6, 9,10,11,12,13. Find
21- QUOTE
(a) 0.2875 (b) 1 (c) QUOTE (d) 0.4286 (e) none of these
22- QUOTE
(a) 0.2875 (b) 1 (c) QUOTE (d) 0.4286 (e) none of these
Suppose that 10% of television sets that are produced from a certain factory are defective. If the worker decides to check each television set before he pack it to remove the defective one. Then
23- The probability that the third television set be removed will be in the fifth check is
(a) 0.0486 (b) 0.0049 (c) 0.0729 (d) 0.0009 (e) none of these
A patient is as likely to go to a certain dental clinic by car as to go on foot in a certain day. If he went to this clinic 7 times. Let X= number he goes by car of these 7 times, then
24-The probability density function of X, is
(a) QUOTE (b) QUOTE
(c) QUOTE (d) QUOTE /X!
(e) none of these
25-The possible value of X are
(a) X=1,2,,7 (b) X=0,1,2,,7 (c) X=0,1 (d) X=1,2,3, (e) none of these
26-The probability that at most one time he goes by car is
(a) 0.1049 (b) 0.9922 (c) 0.0625 (d) 0.9375 (e) none of these
27- The expected value of X, E(X) is
(a) 2 (b) 1.7 (c) 3 (d) 3.5 (e) none of these
In a certain hospital, suppose X represents the number of patients with side effect after taken a medicine for a week has a Poisson (2.5) distribution. Then
28-The probability that three patients have side effect after taken a medicine for a week is
(a) 0.2138 (b) 0.9344 (c) 0.7576 (d) 0.0867 (e) none of these
29-The probability that more than two patients have side effect after taken a medicine for 2 week is
(a) 0.0404 (b) 0.1247 (c) 0.8753 (d) 0.9596 (e) none of these
30- The variance of X is
(a) 5 (b) 1.44 (c) 2.5 (d) 6.25 (e) none of these
Suppose that the distribution function of Y is given by
EMBED Equation.3
31- f(5)=
(a) 0.2 (b) 0.4 (c) 0.6 (d) 0.8 (e) none of these
32- QUOTE
(a) 0 (b) 0.2 (c) 0.6 (d) 0.8 (e) none of these
33- QUOTE
(a) 0 (b) 0.4 (c) 0.8 (d) 1 (e) none of these
34- QUOTE
(a) 0.2 (b) 0.4 (c) 0.6 (d) 0.8 (e) none of these
Take X as a random variable with the following mass function
QUOTE Then,
35- The value of the constant K is
(a) 0.083 (b) 0.25 (c) 0.12 (d) 4 (e) none of these
Suppose that 2% of the items made by a factor are defective. Then
36-The probability that there are 3 defective items in a sample of 100 items is
(a) 0.23 (b) 0.18 (c) 0.13 (d) 0.876 (e) none of these
- Let X and Y are two random variables having the joint probability density function
Y X-32410.20.10.230.10.20.2
P(X+Y ( 3)=
(a) 0.3 (b) 0.6 (c)0.4 (d) 0.8 (e) none of these
f(x=2| y=1)=
(a) 0.4 (b) 0.2 (c) 1 (d) 0.667 (e) none of these
P(X=4,Y(3)=
(a) 1 (b) 0.2 (c) 0.4 (d) 0.3 (e) none of these
E(X|Y=1)=
(a) 0.4 (b) 1.8 (c) 0.8 (d) 0.2 (e) none of these
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