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A pair of dice is thrown. If sum of the numbers is an even number, what is the probability that it is a perfect square?
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In an examination, 30% of students have failed in subject I, 20% of the students have failed in subject II and 10% have failed in both subject I and subject II. A student is selected at random, what is the probability that the student has failed in subject I, if it is known that he is failed in subject II?
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In an examination, 30% of students have failed in subject I, 20% of the students have failed in subject II and 10% have failed in both subject I and subject II. A student is selected at random, what is the probability that the student has failed in at least one subject?
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In an examination, 30% of students have failed in subject I, 20% of the students have failed in subject II and 10% have failed in both subject I and subject II. A student is selected at random, what is the probability that the student has failed in exactly one subject?
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A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that, first is white and second is black?
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A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that, one is white and other is black?
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An urn contains 4 black, 5 white, and 6 red balls. Two balls are drawn one after the other without replacement, What is the probability that at least one ball is black?
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Two balls are drawn from an urn containing 5 green, 3 blue, and 7 yellow balls one by one without replacement. What is the probability that at least one ball is blue?
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The data gives number of accidents per day on a railway track. Compute Q2, P17, and D7.
4, 2, 3, 5, 6, 3, 4, 1, 2, 3, 2, 3, 4, 3, 2.
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The distribution of daily sales of shoes (size-wise) for 100 days from a certain shop is:
| Size of shoes | 2 | 4 | 3 | 5 | 7 | 6 | 8 |
| No. of days | 14 | 20 | 13 | 19 | 13 | 13 | 8 |
Compute Q2, D1, and P95.
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In the frequency distribution of families given below, the number of families corresponding to expenditure group 2000 - 4000 is missing from the table. However value of 25th percentile is 2880. Find the missing frequency.
| Weekly Expenditure (₹1000) | 0 – 2 | 2 – 4 | 4 – 6 | 6 – 8 | 8 – 10 |
| No. of families | 14 | ? | 39 | 7 | 15 |
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Calculate Q1, D6, and P15 for the following data:
| Mid value | 25 | 75 | 125 | 175 | 225 | 275 |
| Frequency | 10 | 70 | 80 | 100 | 150 | 90 |
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Daily income for a group of 100 workers are given below:
| Daily income (in₹) | 0 – 50 | 50 – 100 | 100 – 150 | 150 – 200 | 200 – 250 |
| No. of persons | 7 | ? | 25 | 30 | ? |
P30 for this group is ₹ 110. Calculate the missing frequencies.
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The distribution of a sample of students appearing for a C.A. examination is:
| Marks | 0 – 100 | 100 – 200 | 200 – 300 | 300 – 400 | 400 – 500 | 500 – 600 |
| No. of students | 130 | 150 | 190 | 220 | 280 | 130 |
Help C.A. institute to decide cut-off marks for qualifying an examination when 3% of students pass the examination.
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Find Q1, D6, and P78 for the following data:
| C.I. | 8 – 8.95 | 9 – 9.95 | 10 – 10.95 | 11 – 11.95 | 12 – 12.95 |
| f | 5 | 10 | 20 | 10 | 5 |
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The mean and standard deviations of two brands of watches are given below:
| Brand-I | Brand-II | |
| Mean | 36 months | 48 months |
| S.D. | 8 months | 10 months |
Calculate a coefficient of variation of the two brands and interpret the results.
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Calculate coefficient of variation for the data given below [Given : `sqrt(3.3)` = 1.8166]
| C.I. | 5 – 15 | 15 – 25 | 25 – 35 | 35 – 45 | 45 – 55 | 55 – 65 | 65 – 75 |
| f | 6 | 7 | 15 | 25 | 8 | 18 | 21 |
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Calculate the correlation coefficient from the following data, and interpret it.
| X | 1 | 3 | 5 | 7 | 9 | 11 | 13 |
| Y | 12 | 10 | 8 | 6 | 4 | 2 | 0 |
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Calculate the correlation coefficient from the following data and interpret it.
| x | 9 | 7 | 6 | 8 | 9 | 6 | 7 |
| y | 19 | 17 | 16 | 18 | 19 | 16 | 17 |
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If (x – 1, y + 4) = (1, 2) find the values of x and y.
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