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Q1. You reach your hand into a bag of Scrabble tiles. You pull out one tile and find it has letter A. You pull out one more tile. What is the probability that it will be a letter Z?

Solution

There is a  chance that the first tile will be an A.But once you have that tile, there are only 25 left. So, the probability of the second tile being a Z =

Q2. Sum of the probability of happening and not happening of an event is:

• 1) 1
• 2) 0
• 3) None of these
• 4) 2

Solution

A probability of 0 means that an event is impossible and a probability of 1 means that an event is certain. Therefore, the sum of happening and not happening of an event = 1

Q3. A pair of dice was rolled 5350 times. A pair of 5's occurred 140 times. What is the empirical probability of a pair of 5's?

Solution

Q4. A die is thrown 400 times. The frequency of the outcomes of the events are given as under: Outcomes 1 2 3 4 5 6 Frequency 70 65 60 75 62 68 Find the probability of: (i) Occurrence of an even number. (ii) Occurrence of a number less than 2.

Solution

Total number of frequencies = 400 (i) Even numbers are = 2, 4, 6 Therefore frequencies of all even numbers = 65 + 75 + 68 = 208 Probability of occurrence of an even number (ii) Probability of getting a number less than 2 =

Q5. Which one of the following cannot be the probability of an event?

• 1) 0
• 2)
• 3)
• 4) 1

Solution

_{The probability of an event lies between 0 and 1. Hence, it cannot be negative. Therefore,  is not a possible probability of an event.}

Q6. Following distribution gives the weight of 38 students of a class. Weight in kg. 31 - 35 36 - 40 41 - 45 46 - 50 51 - 55 56 - 60 61 - 65 66 - 70 71 - 75 No. of students 9 5 14 3 1 2 2 1 1 Find the probability that weight of student in the class is (i) at most 60 kg. (ii) at least 36 kg. (iii) not more than 50 kg.

Solution

Total number of students = 38 (i) Number of students whose weight is at most 60 kg = 9 + 5 + 14 + 3 + 1 + 2 = 34 Probability that weight of student is at most 60 kg  (ii) No. of students whose weight is at least 36 kg = 5 + 14 + 3 + 1 + 2 + 2 + 1 + 1 = 29 Probability that the weight of a student is at least 36 kg = (iii) No. of students whose weight is not more than 50 kg = 9 + 5 + 14 + 3 = 31 Probability that the weight of a student is not more than 50 kg = 

Q7. In a survey, out of 200 students, it is observed that 125 students like mathematics. What is the probability of the students who do not like mathematics?

• 1)
• 2)
• 3)
• 4)

Solution

_{Total number of students = 200 Number of students who like Mathematics = 125 Number of students who do not like Mathematics = 200 - 125 = 75 P(do not like Mathematics) =}

Q8.

Solution

(i) P(at least two heads ) =  (ii) P(3 tails) = P(no head) =  (iii) P(at most one head) = 

Q9. The age (in years) of workers are as follows: Age (in yrs) 10 - 19 20 - 29 30 - 39 40 - 49 50 - 59 60 and above No. of workers 5 40 26 15 8 6 If a worker is selected at random, find the probability that the person is: (a) 30 years or more (b) below 50 years

Solution

Total no. of workers = 100 (a) Number of workers who are 30 years or more = 26 + 15 + 8 + 6 = 55 P(30 yrs or more) = (b) Number of workers who are below 50 years = 5 + 40 + 26 + 15 = 86 P(below 50 yrs) =

Q10.

Solution

Q11. In making a math project, a teacher found out that 26 people took two to three hours, 14 people took three to four hours and 10 people took more than four hours to complete a particular assignment. What is the experimental probability that the assignment can be done in less than four hours?

Solution

Q12. Two dice are thrown simultaneously 500 times. Each time the sum of two numbers appearing on them is noted and recorded in the following table:  Sum  2 3 4 5 6 7 8 9 10 11 12 Frequency 14 30 42 55 72 75 70 53 46 28 15 From the above data, what is the probability of getting a sum (i) more than 10 (ii) between 8 and 12.

Solution

Total number of trials = 500 (i) P(sum more than 10) = (ii) P(sum between 8 and 12) =

Q13.

Solution

Q14. The percentage of marks obtained by a student in monthly unit test are given below: Unit Test 1 II III IV V % Marks 70 72 65 68 85 Find the probability that the student gets (a) more than 70% marks (b) more than 90% marks

Solution

Total number of tests = 5 (a) Marks greater than 70% = 72 and 85, hence in 2 tests. P(student gets more than 70% marks) = (b) Marks more than 90 = 0, hence in 0 tests. P(student gets more than 90% marks) =

Q15.

Solution

Q16. A survey at a university was conducted among 880 students. Of these, 500 identified themselves as "smokers". Compute the empirical probability that a randomly selected student is not from a "smoker".

Solution

Q17. A bag contains cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that selected card bears number which is multiple of 2 or 3.

Solution

Total number of outcomes = 25 Multiples of 2 or 3 between 1 and 25 are 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20 ,21, 22, 24 Number of favourable outcomes = 16 P(E) =

Q18. In a survey of 364 children aged 2-4 years, it was found that 91 liked to eat potato chips. If a child is selected at random, the probability that he/she does not like to eat potato chips is:

• 1) 0.75
• 2) 0.25
• 3) 0.50
• 4) 0.80

Solution

Out of 364 children, 91 like to eat potato chips. Number of children who do not like to eat potato chips = 364 - 91 = 273 Probability of children who do not like to eat potato chips = = 0.75

Q19. The following data shows the blood groups of 40 students of a class: Blood group A AB B O No. of students 10 15 12 3 A student is selected at random from the class. Find the probability that the child: (i) has blood group A (ii) has blood group O (iii) does not have blood group AB

Solution

Q20. A survey of 10 student is done regarding the likes and dislike about the subject mathematics. The data are given below: Views Number of students Likes 80 Dislikes 20 Find the probability that a student chosen randomly (a) likes mathematics (b) does not like mathematics

Solution

Total students = 100 (i) P(like Mathematics) = (ii) P(dislike Mathematics) =

Q21.

Solution

(a) Let E be the event that student is from grade 3. Then, P(E) =  (b) Let F be the event that student is not in grade 2, 3, 4, 5 or grade 6. i.e. student is in grade 1 Thus, P(F) = 

Q22. In an experiment, 100 drawing pins were dropped on a floor. 73 landed point up and the rest landed point down. A pin is selected at random and dropped. What is the probability that the pin will land point down?

• 1) 0.27
• 2) 0.73
• 3) 0.72
• 4) 0.37

Solution

Number of pins landing point down = 100 - 73 = 27 Probability of pin landing point down =  = 0.27

Q23.

Solution

Q24. Three unbiased coins are tossed together. Find the probability of getting (i) Two heads (ii) At least two heads (iii) No head

Solution

Sample cases = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} = 8 cases (i) P(two heads) = (ii) P(at least 2 heads) = (iii) P(No head) =

Q25.

Solution

Q26. The weekly pocket money of students are given in the following table:  Pocket Money (in Rs) Number of students 145 7 140 4 159 10 171 6 158 3 147 8 165 12 Find the probability that the weekly pocket money of a student is: (a) Rs 159 (b) more than Rs 159 (c) Less than Rs 159

Solution

Total number of students = 50 (a) P(weekly pocket money of student is Rs 159) = (b) P(weekly pocket money of student is more than Rs 159) =   (c) P (weekly pocket money of student is less than Rs 159) =

Q27. In a medical examination of students of a class, the following blood groups were recorded:

Solution

Q28.

Solution

Q29. When a thumbtack is tossed, there are two possible outcomes. If the empirical probability of "point up" is fixed to be 0.73, what should be the probability of "point down"?

Solution

P(point up) = 0.73P(point down) 1 - 0.73 = 0.27(Since, the sum of probabilities is 1)

Q30. A bag contains 12 balls out of which x are white. If one ball is taken out from the bag, find the probability of getting a white ball. If 6 more white balls are added to the bag and the probability now for getting a white ball is double the previous one, find the value of x.

Solution

No. of white balls = x Total no. of balls = 12 P(white ball) = If 6 white balls are added: Total balls = 18 White balls = x + 6 _{According to the question:}

Q31.

Solution

Q32.

Solution

Q33.

Solution

Total number of tosses = 200 P(two headscome up) = 

Q34.

Solution

Q35. In a sample survey of 640 people, it was found that 400 people have a secondary school certificate. If a person is selected at random, the probability that the person does not have such certificate is

• 1) 0.375
• 2) 0.875
• 3) 0.625
• 4) 0.725

Solution

People having secondary school certificate = 400 People who do not have secondary school certificate = 640 - 400 = 240 Therefore, probability that the person selected does not have the certificate

Q36. One card is drawn at random from a well shuffled deck of 52 cards. Find the probability for getting a face card.

Solution

Here favourable outcomes = 4(Kings) + 4(Queens) + 4(Jacks) = 12 Total number of equally likely cases = 52 Thus, Required probability = 

Q37. Two dice are thrown 400 times. Each time sum of two numbers appearing on their tops is noted as given in the following table: Sum 2 3 4 5 6 7 8 9 10 11 12 Frequency 14 20 32 45 62 65 60 43 36 18 5 What is the probability of getting a sum (i) 5 ? (ii) more than 10 ? (iii) between 5 and 10?

Solution

(i) P(5) = (ii) P(more than 10) = (iii) P(between 5 and 10) = 

Q38.

Solution

When three coins are tossed simultaneously, 

Q39.

Solution

Q40.

Solution

Q41. Two coins are tossed simultaneously 1000 times with the following frequencies of different outcomes: Outcomes 2 Heads 1 Head No Head Frequency 190 560 250 Find the probability of occurrence of each of these events.

Solution

P (2 heads) = P (1 head) = P (no head) =

Q42. Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes: Outcomes 3 heads 2 heads 1 head No heads Frequency 23 72 77 28 Find the probability of getting (i) 3 heads (ii) at least two heads (iii) two heads and one tail.

Solution

Total number of trials = 200 (i) P(getting 3 heads) = (ii) P(at least two heads) =  (iii) P(two heads and one tail) = 

Q43. Fifty seeds were selected at random from each of the 5 bags of seeds and kept under standardized conditions favorable for germination. After 20 days the number of seeds which had germinated in each collection were counted and recorded as follows: Bags 1 2 3 4 5 Number of seeds Germinated 40 48 42 39 41 What is the probability of germination of: (i) More than 40 seeds in a bag? (ii) 49 seeds in a bag? (iii) More than 35 seeds in a bag?

Solution

(i) P(more than 40 seeds in a bag) = (ii) P(49 seeds in a bag) = (iii) P(more than 35 seeds) =

Q44. Following table shows the marks obtained by 30 students in a class test: Marks Obtained 70 58 60 52 65 75 68 Number of Students 3 5 4 7 6 2 3 Find the probability that a student secures (a) 60 marks (b) less than 60 marks.

Solution

Total no. of students = 30 (a) Probability of a student getting 60 marks = (b) Number of students who got less than 60 marks = 5 + 7 = 12 Probability of a student getting less than 60 marks =