probability

Bag I contains 4 white and 6 black balls. Bag II contains 4 white and 3 black balls. One ball is drawn at random from any one of the two bags and it is found to be a black ball. Th...

The probability (in %) that a storm having return period of 15 years may occur in the next 10 years is ________ (rounded off to two decimal places).

The age (in years) of a population is normally distributed with a mean of 36 and standard deviation of 12. The height (in cm) of the same population is also normally distributed wi...

X is a random variable that can take any one of the values 0, 1, 7, 11, and 12. The probability mass function for X is P(X = 0) = 0.4; P(X = 1) = 0.3; P(X = 7) = 0.1; P(X = 11) = 0...

Given that A and B are not null sets, which of the following statements regarding probability is/are CORRECT?

Consider a discrete random variable X whose probabilities are given below. The standard deviation of the random variable is ________ (round off to one decimal place). xi | 1 | 2 |...

A one-way, single lane road has traffic that consists of 30% trucks and 70% cars. The speed of trucks (in km/h) is a uniform random variable on the interval (30, 60), and the speed...

Given that $A$ and $B$ are not null sets, which of the following statements regarding probability is/are CORRECT?

Three distinct sets of indistinguishable twins are to be seated at a circular table that has 8 identical chairs. Unique seating arrangements are defined by the relative positions o...

The probability that a student passes only in Mathematics is $\frac{1}{3}$. The probability that the student passes only in English is $\frac{4}{9}$. The probability that the stude...

In a sample of 100 heart patients, each patient has 80% chance of having a heart attack without medicine X. It is clinically known that medicine X reduces the probability of having...

The return period of a large earthquake for a given region is 200 years. Assuming that earthquake occurrence follows Poisson's distribution, the probability that it will be exceede...

The probability that a student passes only in Mathematics is $\frac{1}{3}$. The probability that the student passes only in English is $\frac{4}{9}$. The probability that the stude...

The return period of a large earthquake for a given region is 200 years. Assuming that earthquake occurrence follows Poisson’s distribution, the probability that it will be exceede...

In a sample of 100 heart patients, each patient has 80% chance of having a heart attack without medicine X. It is clinically known that medicine X reduces the probability of having...

There are 4 red, 5 green, and 6 blue balls inside a box. If N number of balls are picked simultaneously, what is the smallest value of N that guarantees there will be at least two...

A remote village has exactly 1000 vehicles with sequential registration numbers starting from 1000. Out of the total vehicles, 30% are without pollution clearance certificate. Furt...

The probabilities of occurrences of two independent events A and B are 0.5 and 0.8, respectively. What is the probability of occurrence of at least A or B (rounded off to one decim...

The probabilities of occurrences of two independent events A and B are 0.5 and 0.8, respectively. What is the probability of occurrence of at least A or B (rounded off to one decim...

A remote village has exactly 1000 vehicles with sequential registration numbers starting from 1000. Out of the total vehicles, 30% are without pollution clearance certificate. Furt...

A pair of six-faced dice is rolled thrice. The probability that the sum of the outcomes in each roll equals 4 in exactly two of the three attempts is ____________. (round off to th...

At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively...

At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively...

A pair of six-faced dice is rolled twice. The probability that the sum of the outcomes in each roll equals 4 in exactly two of the three attempts is _________ (round off to three d...

A flood control structure having an expected life of n years is designed by considering a flood of return period T years. When T = n, and n $$\to$$ $$\infty$$, the structures hydro...

Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:

In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and...

Contractor X is developing his bidding strategy against Contractor Y. The ratio of Y's bid price to X's cost for the 30 previous bids in which Contractor X has competed against Con...

Vehicular arrival at an isolated intersection follows the Poisson distribution. The mean vehicular arrival rate is 2 vehicle per minute. The probability (round off to two decimal p...

The probability that a 50 year flood may NOT occur at all during 25 years life of a project (round off to two decimal places), is _________.

The probability that the annual maximum flood discharge will exceed 25000 m³/s, at least once in next 5 years is found to be 0.25. The return period of this flood event (in years,...

The probability density function of a continuous random variable distributed uniformly between x and y (for y > x) is

A three-member committee has to be formed from a group of 9 people. How many such distinct committees can be formed?

Probability (up to one decimal place) of consecutively picking 3 red balls without replacement from a box containing 5 red balls and 1 white ball is _________

A two-faced fair coin has its faces designated as head (H) and tail (T). This coin is tossed three times in succession to record the following outcomes: H, H, H. If the coin is tos...

Vehicles arriving at an intersection from one of the approach roads follow the Poisson distribution. The mean rate of arrival is 900 vehicles per hour. If a gap is defined as the t...

A two-faced fair coin has its faces designated as head $$(H)$$ and tail $$(T)$$. This coin is tossed three times in succession to record the following outcomes: $$H, H,H.$$ If the...

The number of parameters in the univariate exponential and Gaussian distributions, respectively, are

$$X$$ and $$Y$$ are two random independent events. It is known that $$P(X)=0.40$$ and $$\,P\left( {X \cup {Y^C}} \right) = 0.7.$$ Which one of the following is the value of $$P\lef...

Four cards are randomly selected from a pack of $$52$$ cards. If the first two cards are kings, what is the probability that the third card is a king?

An observer counts $$240$$veh/h at a specific highway location. Assume that the vehicle arrival at the location is Poisson distributed, the probability of having one vehicle arrivi...

A traffic office imposes on an average $$5$$ number of penalties daily on traffic violators. Assume that the number of penalties on different days is independent and follows a Pois...

A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes; (i) Head, (ii) Head, (III) Head, (iv) Head. The probability of obtaining a ''Tail...

A 1-hour rainfall of 10 cm has a return period of 50 years. The probability that 1 hour of rainfall 10 cm or more will occur in each of two successive years is

Is an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is

The annual precipitation data of a city is normally distributed with mean and standard deviation as $$1000$$mm and $$200$$ mm, respectively. The probability that the annual precipi...

There are two containers with one containing $$4$$ red and $$3$$ green balls and the other containing $$3$$ blue balls and $$4$$ green balls. One ball is drawn at random from each...

Two coins are simultaneously tossed. The probability of two heads simultaneously appearing

The standard normal probability function can be approximated as $$$F\left( {{X_N}} \right) = {1 \over {1 + \exp \left( { - 1.7255{X_N}{{\left| {{X_N}} \right|}^{0.12}}} \right)}}\,...

A hydraulic structure has four gates which operate independently. The probability of failure of each gate is $$0.2.$$ Given that gate $$1$$ has failed, the probability that both ga...

A box contains $$10$$ screws, $$3$$ of which are defective. Two screws are drawn at random with replacement. The probability that none of the two screws is defective will be

The return period for the annual maximum flood of a given magnitude is 8 years. The probability that this flood magnitude will be executed once during the next 5 years is