The record of a weather station shows that out of the past 250 consecutive days, its weather forecast were correct 175 times. What is the probability that on a given day (i) it was correct? (ii) it was not correct?

The record of a weather station shows that out of the past 250 onsecutivedays, its weather forecasts were correct 175 times.(i) What is the probability that on a given day it was correct?(ii) What is the probability that it was not correct on a given day?

In a school, 300 students were surveyed. The survey showed that 186 students liked watching cricket match while the rest disliked it. Out of these students, if one student is chosen at random, what is the probability that the chosen student : (i) likes watching cricket match? (ii) dislikes watching cricket match?

Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on (i) the same day? (ii) consecutive days? (iii) different days?

The same 20 contestants, on each of 3 days, answered 5 questions in order to win a prize. Each contestant received 1 point for each correct answer. The number of contestants receiving a given score on each day is shown in the table above. No contestant received the same score on two different days. If a contestant is selected at random, what is the probability that the selected contestant received a score of 5 on Day 2 or Day 3, given that the contestant received a score of 5 on one of the three days?

On a particular day, at a crossing in a city, the various types of 280 vehicles going past during a time interval were observed as under: |{:("Type of vehicle","Two wheelers","Three wheelers","Four wheelers"),("Frequency"," 91"," 63"," 126"):}| Out of these vechicles , one is chosen at random, what is the probability that the chosen vechicle is (i) a four wheeler (ii) a two wheeler (iii) a three wheeler?

. In a class test containing 10 questions, 5 marks are awarded for every correct answer and (-2) marks are awarded for every incorrect answer and 0 for questions not attempted. (i) Mohan gets four correct and six incorrect answers. What is his score? (ii) Reshma gets five correct answers and five incorrect answers, what is her score? (iii) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?

Two dice are thrown simultaneouly 500 times. Each time the sum of the two numbers appearing on their tops is noted and recorded as given in the following table If the dice are thrown once more, then what is probability of getting a sum i) 3? ii) More than 10? iii) Less than or equal to 5? iv) Between 8 and 12?

(i) Show dimensionally that the equation of the time period of a simple pendulum of length l. Given relation T=2pil//g is incorrect. (ii) Find its correct form.

In an automobile factory, certain parts are to be fixed into the chassis in a section before it moves into another section. On a given day, one of the three persons A, B and C carries out this task. A has 45% chance, B has 35% chance and C has 20% chance of doing the task. The probability that A, B and C will take more than the allotted time is (1)/(6), (1)/(10) and (1)/(20) respectively. If it is found that the time taken is more than the allotted time, what is the probability that A has done the task ?

The same 20 contestants, on each of 3 days, answered 5 questions in order to win a prize. Each contestant received 1 point for each correct answer. The number of contestants receiving a given score on each day is shown in the table above. What was the mean score of the contestants on Day 1 ?