These are Multiple Choice Questions (MCQ) from Exams posted before May 2024. These MCQs get orphaned after the system upgrade.
An airline company known for its promo fare receives on an average 9.7 complaints per day. Using Poisson probability distribution formula, find the probability that on a certain day this airline company will receive exactly 8 complaints.
In a gambling game a man is paid \$50 if he gets all heads or all tails when 3 coins are tossed, and he pays out \$30 if either 1 or 2 heads show. What is his expected gain?
A three-man jury has two members each of whom independently has a probability p of making the correct decision and a third member who flips a coin for each decision (majority rules).
Find the probability that a person tossing three coins will get either all heads or all tails for the second time on the fifth toss.
In the CE Board examinations, the probability that an examinee will pass in each subject is 0.80. What is the probability that the examinee will pass at least two subject?
The drainage from a community during a storm is a normal random variable estimated to have a mean of 1.2 million gallons per day (mgd) and a standard deviation of 0.4 mgd.
An urn contains 6 red marbles and 4 black marbles. Two marbles are drawn without replacement from the urn. What is the probability that both of the marbles are black?
A student goes to the library. The probability that she checks out (a) a work of fiction is 0.40, (b) a work of non-fiction is 0.30, and (c) both fiction and non-fiction is 0.20. What is the probability that the student checks out a work of fiction, non-f
According to the theory of genetics a certain cross of guinea pigs will result in red, black and white offspring in the ratio 8:4:4. Find the probability that among 8 such offspring 5 will be red, 2 black and 1 white.
Evaluate 2000C2 + 2000C5 + 2000C8 + ... + 2000C29.
A bag contains 20 tennis balls, of which four are defective. If two balls are selected at random from the bag, what is the probability that both are defective?
A combination lock has 60 different positions. To open the lock, the dial is turned to a certain number in the clockwise direction, then to a number in the counterclockwise direction, and finally to a third number in the clockwise direction.
Find the probability that in a group of eight students at least two people have the same birthday.
A disease is known to affect 1 in 10,000 people. It can be fatal, but it is treatable if it is detected early. A screening test for the disease shows a positive result for 99% of people with the disease. The test shows positive for 2% of people who do
There are four red, three green, and five blue discs in a bag. Find the probability that two discs of the same color are drawn.
The Department of Health encourages elderly people to have a flu vaccination each year.
3^n - 3^{n - 1} - 3^{n - 2} is equal to:
Simplify the radical shown: $\sqrt{a\sqrt{a\sqrt{a}}}$
If z varies directly as x and inversely as the square of y, and z = 1/3, x = 4, and y = 6, find z when x = 12 and y = 4.
If x varies directly as y and inversely as z and x = 14 when y = 7, and z = 2. Find x when y = 16 and z = 4.
Solve for <em>x</em> if $\dfrac{3(2x - 1)^{1/2}}{x - 3} - \dfrac{(2x - 1)^{3/2}}{(x - 3)^2} = 0$
Is x - 2 a factor of x^3 - 3x^2 + 7x - 10?
Using synthetic division, find the quotient if 2x^3 - 9x^2 + 10x - 3 is divided by x - 3.
Find the quotient of x^3 - x^2 - 5x + 6 divided by x - 2.
When x^2 + 5x - 2 is divided by x + n, the remainder is -8. Find all possible values of n.
Solve for x from the given equation: 2^x · 2^(x + 1) = 128.
Solve for x if $x = \log \left[ 10 \log (5 \log 100) \right]^3$.
Solve for x if $\dfrac{e^x + e^{-x}}{2} = 1$.
Solve for y if $y = (e^x + e^{-x})^2 - (e^x - e^{-x})^2$.
Solve for y if $y = e^{\ln \sqrt{x}}$.
Solve for x if $\ln e^{\sqrt{x + 1}} = 3$.
Without the use of calculator, solve for y if $\ln y = \frac{1}{2}\ln 4 + \frac{2}{3} \ln 8$.
Solve for x if $e^{\ln (1 - x)} = 2x$.
Solve for x if $\ln x = 2 + \ln (1 - x)$.
Solve for x if $e^{\ln (2x - 1)} = 5$.
Solve for x if $e^{2x - 1} = 5$.
Solve for x if $ln (x + 1) = 0$.
Simplify and solve for y: $y = \ln \left( \dfrac{e^x}{e^{x - 1}} \right)$.
Simplify and solve for y: $y = \ln \left( \dfrac{e^x}{e^{x - 1}} \right)$.
Simplify and solve for y: $y = \ln \left( \dfrac{e^x}{e^{x - 1}} \right)$.
Simplify and solve for y: $y = \ln \left( \dfrac{e^x}{e^{x - 1}} \right)$.
The sum and product of three distinct positive integers are 15 and 45, respectively. What is the smallest integer?
The sum of thirteen consecutive integers is zero. What is the smallest integer?
X and Y are inversely proportional with each other. Given that X = 15,000 when Y = 162,500. Find X when Y = 328,400.
What is the value of $x - y$ from the following linear equations? $3x + 2y = 2$, $6x - 5y = -32$
Solve for $x^2$ if $48^{1/x} = 4 \times 3^{1/x}$.
Given the following equations: $ab = 1/8$, $ac = 3$, $bc = 6$. Find the value of $b$.
What is the coefficient of the term involving $x^{-3}$ in the expansion of $\left( 2x + \dfrac{2}{x} \right)^5?
The polynomial $x^3 + 4x^2 - 3x + 8$ is divided by $x - 5$. What is the remainder?
If a car can travel x km in y hours, how many hours can it travel a distance of z km?