It is estimated that average number of events during an year is three. What is the probability of occurrence of not more than two events over a two year duration? Assume that the number of events follow a Poisson's distribution.

0.052

0.062

0.072

0.082

Correct Answer: 0.062

The following are the two statements relating to the theory of probability. Indicate the statements being correct or incorrect.
Statement I The probability of the joint occurrence of independent events A and B is equal to the probability of event A multiplied by the probability of event B or vice-versa.
Statement II The probability of the joint occurrence of independent event A and dependent event B is equal to the probability of event A multiplied by the conditionalprobability of event B when event A has occurredor vice-versa.

Both statements are correct

Both statements are incorrect

Statement I is correct while Statement II is incorrect

Statement I is incorrect while Statement II is correct

Which of the following statements are true?
1. The classical approach to probability theory requires that the total number of possible outcomes be known or calculated and that each of the outcomes be equally likely.
2. A marginal probability is also known as unconditional probability.
3. For three independent events, the joint probability of the three events, P (ABC) = P (A) × P (B/A) × P (C/AB)
4. Two events are mutually exclusive, exhaustive and equally likely, the probability of either event A or B or both occurring P(A or B) = P(A) + P(B)

Both 1 and 3

Both 3 and 4

1, 2 and 4

All of the above

A probability distribution with right skew is shown in the figure.

The correct statement for the probability distribution is

Mean is equal to mode

Mean is greater than median but less than mode

Mean is greater than median and mode

Mode is greater than median

Which of the following statements are true/false?
1. Every worker who has worked fora period of 240 days or more in a factory during a calendar year shall be allowed during the subsequent calendar year, leave with wages.
2. A worker who has been allowed leave for not less than four days, in the case of an adult, and five days, in the case of a child shall, before his leave begins, be paid the wages due for the period of the leave allowed.
3. If a worker works in a factory works for more than nine hours in any day or for more than 40 hours in any week, he shall, in respect of overtime work, be entitled to wagesat the rate oftwicehis ordinary rate of wages.4. The periods of work of an adult worker in a factory shall be so arranged that inclusive of his intervals for rest, they shall not spread over more than eleven and a half hours in any day.

1, 4 are true and 2, 3 are false

1, 2 are true and 3, 4 are false

2, 4 are true and 1, 3 are false

3, 4 are true and 2, 1 are false

In an opencast mine, dumpers arrive at a shovel location with an average arrival rate of 12 per/hour. The inter-arrival times of the dumpers follow an exponential distribution. The service times of the shovel also follow an exponential distribution with an average of 3 minute. The average waiting time of a dumper in the queue in minutes is

2.7

4.5

7.5

Rahim has invited his three buddies over to watch the basketball game on his wide-screen television. They are all hungry, but no one wants to leave to get food. Just as they are arguing about who should make the food run, a commercial comes on for a local pizzeria that delivers. The phone number flashes on the screen briefly and they all try to remember it. By the time Zachary grabs a pen and paper, each of them recollects a different number.i. All of the men agree that the first three numbers are 995.ii. Three of them agree that the fourth number is 9.iii. Three agree that the fifth number is 2.iv. Three agree that the sixth number is 6; three others agree that the seventh number is also 6.Which of the numbers is most likely the telephone number of the pizzeria?

995-9266

995-9336

995-9268

995-8266

Zachary has invited his three buddies over to watch the basketball game on his wide-screen television. They are all hungry, but no one wants to leave to get food. Just as they are arguing about who should make the food run, a commercial comes on for a local pizze-ria that delivers. The phone number flashes on the screen briefly and they all try to remember it. By the time Zachary grabs a pen and paper, each of them recollects a different number.

#1 : All of the men agree that the first three numbers are 995.
#2 : Three of them agree that the fourth number is 9.
#3 : Three agree that the fifth number is 2.
#4 : Three agree that the sixth number is 6; three others agree that the seventh number is also 6.

Which of the numbers is most likely the telephone number of the pizzeria?

995-9266

995-9336

995-9268

995-8266

Simplify : $${{{5 \over 3} \times {7 \over {51}}{\text{ of }}{{17} \over 5} - {1 \over 3}} \over {{2 \over 9} \times {5 \over 7}{\text{ of }}{{28} \over 5} - {2 \over 3}}}$$

$$\frac{1}{2}$$

$$\frac{1}{4}$$

Arrange the following steps in sequence in order to calculate the probability of an event through Naïve Bayes classifier. I. Find the likelihood probability with each attribute for each class. II. Calculate the prior probability for given class labels. III. Put these values in Bayes formula and calculate posterior probability. IV. See which class has a higher probability, given the input belongs to the higher probability class.

I → II → III → IV

II → I → III → IV

III → II → I → IV

II → III → I → IV

A mans average monthly expenditure for the first four months of the year was Rs. 231.25. For the next five months, the average monthly expenditure was Rs. 22.75 more than what it was during the first four months. If the person spent Rs. 605 in all during the remaining three months of the year, find what percentage of his annual income of Rs. 3500 did he save in the year?

10%

15%

20%

25%