UPSC Exam > UPSC Questions > Q.11. If a random variable x assumes the valu...
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Q.11. If a random variable x assumes the values 0, 1 and 2 with probabilities 0.30, 0.50 and 0.20, then its expected
value is
(a) 1.50 (b) 3 (c) 0.90 (d) 1
Q.12. To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample
without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200. Bulbs contains 5
defective bulbs. Find the probability that the sample will be rejected.
(a) 197/3980 (b) 125/3980 (c) 189/3980 (d) None of these.
Q.13. A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected
at random from the packet, what is the probability that the sample does not contain more than 1 defective?
(a) 1/3 (b) 2/3 (c) 13/15 (d) 3/15?
value is
(a) 1.50 (b) 3 (c) 0.90 (d) 1
Q.12. To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample
without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200. Bulbs contains 5
defective bulbs. Find the probability that the sample will be rejected.
(a) 197/3980 (b) 125/3980 (c) 189/3980 (d) None of these.
Q.13. A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected
at random from the packet, what is the probability that the sample does not contain more than 1 defective?
(a) 1/3 (b) 2/3 (c) 13/15 (d) 3/15?
Most Upvoted Answer
Q.11. If a random variable x assumes the values 0, 1 and 2 with probab...
Probability of a Random Variable
The expected value of a random variable is calculated by multiplying each possible value by its probability and then summing up the results. Given that the random variable x assumes the values 0, 1, and 2 with probabilities 0.30, 0.50, and 0.20 respectively, we can calculate the expected value as follows:
Expected value = (0*0.30) + (1*0.50) + (2*0.20) = 0 + 0.50 + 0.40 = 0.90
Therefore, the expected value of the random variable x is 0.90, which corresponds to option (c).
Probability of Sample Rejection
When two bulbs are randomly selected without replacement from a sample of 200 bulbs containing 5 defectives, the probability of the sample being rejected can be calculated as follows:
Probability of both bulbs being defective = (5/200) * (4/199) = 1/199
Probability of at least one bulb being defective = 1 - Probability of both bulbs being non-defective = 1 - (195/200 * 194/199) = 1 - 0.975 = 0.025
Therefore, the probability of the sample being rejected is 0.025, which corresponds to option (a).
Probability of Selecting Components
When selecting 4 components from a packet of 10 components with 2 defectives, the probability of not selecting more than 1 defective component can be calculated as follows:
Probability of selecting 0 defectives = (8/10) * (7/9) * (6/8) * (5/7) = 5/9
Probability of selecting 1 defective = (2/10) * (8/9) * (7/8) * (6/7) = 1/9
Therefore, the probability of not selecting more than 1 defective component is 5/9 + 1/9 = 6/9 = 2/3, which corresponds to option (b).
The expected value of a random variable is calculated by multiplying each possible value by its probability and then summing up the results. Given that the random variable x assumes the values 0, 1, and 2 with probabilities 0.30, 0.50, and 0.20 respectively, we can calculate the expected value as follows:
Expected value = (0*0.30) + (1*0.50) + (2*0.20) = 0 + 0.50 + 0.40 = 0.90
Therefore, the expected value of the random variable x is 0.90, which corresponds to option (c).
Probability of Sample Rejection
When two bulbs are randomly selected without replacement from a sample of 200 bulbs containing 5 defectives, the probability of the sample being rejected can be calculated as follows:
Probability of both bulbs being defective = (5/200) * (4/199) = 1/199
Probability of at least one bulb being defective = 1 - Probability of both bulbs being non-defective = 1 - (195/200 * 194/199) = 1 - 0.975 = 0.025
Therefore, the probability of the sample being rejected is 0.025, which corresponds to option (a).
Probability of Selecting Components
When selecting 4 components from a packet of 10 components with 2 defectives, the probability of not selecting more than 1 defective component can be calculated as follows:
Probability of selecting 0 defectives = (8/10) * (7/9) * (6/8) * (5/7) = 5/9
Probability of selecting 1 defective = (2/10) * (8/9) * (7/8) * (6/7) = 1/9
Therefore, the probability of not selecting more than 1 defective component is 5/9 + 1/9 = 6/9 = 2/3, which corresponds to option (b).
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Q.11. If a random variable x assumes the values 0, 1 and 2 with probabilities 0.30, 0.50 and 0.20, then its expected value is (a) 1.50 (b) 3 (c) 0.90 (d) 1 Q.12. To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200. Bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected. (a) 197/3980 (b) 125/3980 (c) 189/3980 (d) None of these.Q.13. A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective? (a) 1/3 (b) 2/3 (c) 13/15 (d) 3/15?
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Q.11. If a random variable x assumes the values 0, 1 and 2 with probabilities 0.30, 0.50 and 0.20, then its expected value is (a) 1.50 (b) 3 (c) 0.90 (d) 1 Q.12. To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200. Bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected. (a) 197/3980 (b) 125/3980 (c) 189/3980 (d) None of these.Q.13. A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective? (a) 1/3 (b) 2/3 (c) 13/15 (d) 3/15? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q.11. If a random variable x assumes the values 0, 1 and 2 with probabilities 0.30, 0.50 and 0.20, then its expected value is (a) 1.50 (b) 3 (c) 0.90 (d) 1 Q.12. To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200. Bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected. (a) 197/3980 (b) 125/3980 (c) 189/3980 (d) None of these.Q.13. A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective? (a) 1/3 (b) 2/3 (c) 13/15 (d) 3/15? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.11. If a random variable x assumes the values 0, 1 and 2 with probabilities 0.30, 0.50 and 0.20, then its expected value is (a) 1.50 (b) 3 (c) 0.90 (d) 1 Q.12. To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200. Bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected. (a) 197/3980 (b) 125/3980 (c) 189/3980 (d) None of these.Q.13. A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective? (a) 1/3 (b) 2/3 (c) 13/15 (d) 3/15?.
Q.11. If a random variable x assumes the values 0, 1 and 2 with probabilities 0.30, 0.50 and 0.20, then its expected value is (a) 1.50 (b) 3 (c) 0.90 (d) 1 Q.12. To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200. Bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected. (a) 197/3980 (b) 125/3980 (c) 189/3980 (d) None of these.Q.13. A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective? (a) 1/3 (b) 2/3 (c) 13/15 (d) 3/15? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q.11. If a random variable x assumes the values 0, 1 and 2 with probabilities 0.30, 0.50 and 0.20, then its expected value is (a) 1.50 (b) 3 (c) 0.90 (d) 1 Q.12. To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200. Bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected. (a) 197/3980 (b) 125/3980 (c) 189/3980 (d) None of these.Q.13. A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective? (a) 1/3 (b) 2/3 (c) 13/15 (d) 3/15? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.11. If a random variable x assumes the values 0, 1 and 2 with probabilities 0.30, 0.50 and 0.20, then its expected value is (a) 1.50 (b) 3 (c) 0.90 (d) 1 Q.12. To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200. Bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected. (a) 197/3980 (b) 125/3980 (c) 189/3980 (d) None of these.Q.13. A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective? (a) 1/3 (b) 2/3 (c) 13/15 (d) 3/15?.
Solutions for Q.11. If a random variable x assumes the values 0, 1 and 2 with probabilities 0.30, 0.50 and 0.20, then its expected value is (a) 1.50 (b) 3 (c) 0.90 (d) 1 Q.12. To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200. Bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected. (a) 197/3980 (b) 125/3980 (c) 189/3980 (d) None of these.Q.13. A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective? (a) 1/3 (b) 2/3 (c) 13/15 (d) 3/15? in English & in Hindi are available as part of our courses for UPSC.
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Here you can find the meaning of Q.11. If a random variable x assumes the values 0, 1 and 2 with probabilities 0.30, 0.50 and 0.20, then its expected value is (a) 1.50 (b) 3 (c) 0.90 (d) 1 Q.12. To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200. Bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected. (a) 197/3980 (b) 125/3980 (c) 189/3980 (d) None of these.Q.13. A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective? (a) 1/3 (b) 2/3 (c) 13/15 (d) 3/15? defined & explained in the simplest way possible. Besides giving the explanation of
Q.11. If a random variable x assumes the values 0, 1 and 2 with probabilities 0.30, 0.50 and 0.20, then its expected value is (a) 1.50 (b) 3 (c) 0.90 (d) 1 Q.12. To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200. Bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected. (a) 197/3980 (b) 125/3980 (c) 189/3980 (d) None of these.Q.13. A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective? (a) 1/3 (b) 2/3 (c) 13/15 (d) 3/15?, a detailed solution for Q.11. If a random variable x assumes the values 0, 1 and 2 with probabilities 0.30, 0.50 and 0.20, then its expected value is (a) 1.50 (b) 3 (c) 0.90 (d) 1 Q.12. To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200. Bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected. (a) 197/3980 (b) 125/3980 (c) 189/3980 (d) None of these.Q.13. A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective? (a) 1/3 (b) 2/3 (c) 13/15 (d) 3/15? has been provided alongside types of Q.11. If a random variable x assumes the values 0, 1 and 2 with probabilities 0.30, 0.50 and 0.20, then its expected value is (a) 1.50 (b) 3 (c) 0.90 (d) 1 Q.12. To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200. Bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected. (a) 197/3980 (b) 125/3980 (c) 189/3980 (d) None of these.Q.13. A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective? (a) 1/3 (b) 2/3 (c) 13/15 (d) 3/15? theory, EduRev gives you an
ample number of questions to practice Q.11. If a random variable x assumes the values 0, 1 and 2 with probabilities 0.30, 0.50 and 0.20, then its expected value is (a) 1.50 (b) 3 (c) 0.90 (d) 1 Q.12. To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200. Bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected. (a) 197/3980 (b) 125/3980 (c) 189/3980 (d) None of these.Q.13. A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective? (a) 1/3 (b) 2/3 (c) 13/15 (d) 3/15? tests, examples and also practice UPSC tests.
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