**Exercise 25.1**

**Question 1. A coin is tossed 1000 times with the following frequencies:**

**Head: 455, Tail: 545**

**Compute the probability for each event.**

**Solution 1.**

**Question 2. Two coins are tossed simultaneously 500 times with the following frequencies of different outcomes:**

**Two heads: 95 times**

**One tail: 290 times**

**No head: 115 times**

**Find the probability of occurrence of each of these events.**

**Solution 2.**

**Question 3. Three coins are tossed simultaneously 100 times with the following frequencies of different outcomes:**

**If the three coins are simultaneously tossed again, compute the probability of:**

**(i) 2 heads coming up. (ii) 3 heads coming up**

**(iii) at least one head coming up. (iv) getting more heads than tails.**

**(v) getting more tails than heads.**

**Solution 3.**

**Question 4. 1500 families with 2 children were selected randomly and the following data were recorded:**

**If a family is chosen at random, compute the probability that it has:**

**(i) No girl**

**(ii) 1 girl**

**(iii) 2 girls**

**(v) at most one girl**

**(v) more girls than boys**

**Solution 4.**

**Question 5. In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays. Find the probability that on a ball played:**

**(i) he hits boundary.**

**(ii) he does not hit a boundary.**

**Solution 5.**

**Question 6. The percentage of marks obtained by a student in monthly unit tests are given below:**

**Unit test: I II III IV V**

**Percentage of mark obtained: 69 71 73 68 76**

**Find the probability that the student gets:**

**(i) more than 70% marks**

**(ii) less than 70% marks**

**(iii) a distinction.**

**Solution 6.**

**Question 7. To know the opinion of the students about Mathematics, a survey of 200 students was conducted. The data is recorded in the following table:**

**Find the probability that a student chosen at random**

**(i) Likes Mathematics**

**(ii) Does not like it.**

**Solution 7.**

**Question 8. The blood groups of 30 students of class IX are recoded as follows:**

**A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O,**

**A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.**

**A student is selected at random from the class from blood donation. Find the probability that the blood group of the student chosen is:**

**(i) A**

**(ii) B**

**(iii) AB**

**(iv) O**

**Solution 8.**

**Question 9. Eleven bags of wheat flour, each marked 5kg, actually contained the following weights of flour (in kg.):**

**4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00**

**Find the probability that any of these bags chosen at random contains more than 5kg. of flour.**

**Solution 9.**

**Question 10. Following table shows the birth month of 40 students of class IX.**

**Find the probability that a student was born in August.**

**Solution 10.**

**Question 11. Given below is the frequency distribution table regarding the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days.**

**Find the probability of concentration of sulphur dioxide in the interval 0.12-0.16 on any of these days.**

**Solution 11.**

_{2}in the interval) = (Number of Concentration of sulphur dioxide in the interval 0.12-0.16)/(Total number of days)

_{2}in the interval) = 2/30 = 0.06

**Question 12. Companies selected 2400 families at random and survey them to determine a relationship between income level and the number of vehicles in a home. The information gathered is listed in the table below:**

**If a family is chosen, find the probability that the family is:**

**(i) earning Rs 10000-13000 per month and owning exactly 2 vehicles.**

**(ii) earning Rs 16000 or more per month and owning exactly 1 vehicle.**

**(iii) earning less than Rs 7000 per month and does not own any vehicle.**

**(iv) earning Rs. 13000-16000 per month and owning more than 2 vehicles.**

**(v) owning not more than 1 vehicle.**

**(vi) owning at least one vehicle.**

**Solution 12.**

**Question 13. The following table gives the life time of 400 neon lamps:**

**A bulb is selected at random. Find the probability that the life time of the selected bulb is:**

**(i) less than 400**

**(ii) between 300 to 800 hours.**

**(iii) at least 700 hours.**

**Solution 13.**

**Question 14. Given below is the frequency distribution of wages (in Rs.) of 30 workers in a certain factory:**

**A worker is selected at random. Find the probability that his wages are:**

**(i) less than Rs. 150**

**(ii) at least Rs. 210**

**(iii) more than or equal to 150 but less than Rs. 210.**

**Solution 14.**