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Probability Quiz-19

As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background.  Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced..

Q1. A random variable X follows binomial distribution with mean Î± and variance Î².Then
•  0 < Î± < Î²
•  0 < Î² < Î±
•  Î± < 0 < Î²
•  Î² < 0 < Î±
Solution

Q2. A coin is tossed 4 times. The probability that at least one head turns up, is
•  1/16
•  2/16
•  14/16
•  15/16
Solution

Q3. If A and B are arbitrary events, then
• P(A∩B) ≥ P(A) + P(B)
•  P(A∪B) ≤ P(A) + P(B)
•  P(A∩B) = P(A) + P(B)
•  None of the above
Solution

Q4. Two numbers are selected randomly from the set S={1,2,3,4,5,6} without replacement one by one. The probability that minimum of the two numbers is less than, 4 is
•  1/15
•  14/15
•  1/5
•  4/5
Solution

Q5. In a binomial distribution B(n, P=1/4), if the probability of at least one success is greater than or equal to 9/10, then n is greater than
•  1/log10⁡4-log10⁡3
•  1/log10⁡4+log10⁡3
•  9/log10⁡4-log10⁡3
•  4/log10⁡4-log10⁡3
Solution

Q6. A and B are two independent events. The probability that both A and B occur is 1/6 and the probability that neither of them occurs is 1/3. Then,
•  P(A)=1/2,P(B)=1/3
•  P(A)=1/2,P(B)=1/6
•  P(A)=1/3,P(B)=1/6
•  None of these
Solution

Q7. Seven chits are numbered 1 to 7. Four chits are drawn one by one with replacement. The probability that the least number appearing on any selected chit is 5, is
•  (3/7)4
•  (6/7)3
•  (5∙4∙3)/73
•  (3/4)3
Solution

Q8. In a Poisson distribution mean is 16, then standard deviation is
•  16
•  256
•  128
•  4

Solution

Q9. From a group of 8 boys and 3 girls, a committee of 5 members to be formed. Find the probability that 2 particular girls are included in the committee
•  4/11
•  2/11
•  6/11
•  8/11
Solution

Q10. A,B,C are any three events. If P(S) denotes the probability of S happening, then P(A∩(B∪C)) =
•  P(A)+P(B)+P(C)-P(A∩B)-P(A∩C)
•  P(A)+P(B)+P(C)-P(B)P(C)
•  P(A∩B)+P(A∩C)-P(A∩B∩C)
•  P(A)+P(B)+P(C)
Solution

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