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A card is drawn from a well-shuffled pack of 52 cards. Consider two events A and B as
A: a club 6 card is drawn.
B: an ace card 18 drawn.
Determine whether the events A and B are independent or not.
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A bag contains 4 blue and 5 green balls. Another bag contains 3 blue and 7 green balls. If one ball is drawn from each bag, what is the probability that two balls are of the same colour?
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Two cards are drawn one after the other from a pack of 52 cards with replacement. What is the probability that both the cards drawn are face cards?
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Determine graphically the value of median, D3, and P35 for the data given below:
| Class | 10 – 15 | 15 – 20 | 20 – 25 | 25 – 30 | 30 – 35 | 35 – 40 | 40 – 45 |
| Frequency | 8 | 14 | 8 | 25 | 15 | 14 | 6 |
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The I.Q. test of 500 students of a college is as follows:
| I.Q. | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 | 60 – 70 | 70 – 80 | 80 – 90 | 90 – 100 |
| Number of students | 41 | 52 | 64 | 180 | 67 | 45 | 40 | 11 |
Find graphically the number of students whose I.Q. is more than 55 graphically.
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Draw an ogive for the following distribution. Determine the median graphically and verify your result by mathematical formula.
| Height (in cms.) | No. of students |
| 145 − 150 | 2 |
| 150 − 155 | 5 |
| 155 − 160 | 9 |
| 160 − 165 | 15 |
| 165 − 170 | 16 |
| 170 − 175 | 7 |
| 175 − 180 | 5 |
| 180 − 185 | 1 |
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Draw a cumulative frequency curve more than type for the following data and hence locate Q1 and Q3. Also, find the number of workers with daily wages
(i) Between ₹ 170 and ₹ 260
(ii) less than ₹ 260
| Daily wages more than (₹) | 100 | 150 | 200 | 250 | 300 | 350 | 400 | 450 | 500 |
| No. of workers | 200 | 188 | 160 | 124 | 74 | 49 | 31 | 15 | 5 |
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Draw ogive of both the types for the following frequency distribution and hence find median.
| Marks | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 | 60 – 70 | 70 – 80 | 80 – 90 | 90 – 100 |
| No. of students | 5 | 5 | 8 | 12 | 16 | 15 | 10 | 8 | 5 | 2 |
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For a distribution, Q1 = 25, Q2 = 35 and Q3 = 50. Find Bowley’s coefficient of skewness Skb.
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For a distribution Q3 – Q2 = 40, Q2 – Q1 = 60. Find Bowley’s coefficient of skewness Skb.
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For a distribution, Bowley’s coefficient of skewness is 0.6. The sum of upper and lower quartiles is 100 and median is 38. Find the upper and lower quartiles.
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Calculate Bowley’s coefficient of skewness Skb from the following data:
| Marks above | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |
| No. of students | 120 | 115 | 108 | 98 | 85 | 60 | 18 | 5 | 0 |
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Find Skb for the following set of observations:
18, 27, 10, 25, 31, 13, 28.
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Following table shows how the samples of Mathematics and Economics scores of 25 students are distributed:
| Marks in Economics | Marks in Mathematics | |
| 40 – 70 | 70 – 100 | |
| 40 – 70 | 20 | 15 |
| 70 – 100 | 5 | 10 |
Find the value of χ2 statistic.
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Compute χ2 statistic from the following data:
| Graduates | Post-Graduates | |
| Male | 28 | 22 |
| Female | 32 | 18 |
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Attitude of 250 employees towards a proposed policy of the company is as observed in the following table. Calculate the χ2 statistic.
| Favor | Indifferent | Oppose | |
| Male | 68 | 46 | 36 |
| Female | 27 | 49 | 24 |
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In a certain sample of 1000 families, 450 families are consumers of tea. Out of 600 Hindu families, 286 families consume tea. Calculate the χ2 statistic.
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A sample of boys and girls were asked to choose their favourite sport, with the following results. Find the value of the χ2 statistic.
| Football | Cricket | Hockey | Basketball | |
| Boys | 86 | 60 | 44 | 10 |
| Girls | 40 | 30 | 25 | 5 |
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A box contains 25 tickets numbered 1 to 25. Two tickets are drawn at random. What is the probability that the product on the numbers is even?
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Two throws are made, the first with 3 dice and the second with 2 dice. The faces of each die are marked with the number 1 to 6. What is the probability that the total in first throw is not less than 15 and at the same time the total in the second throw is not less than 8?
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