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Probability Quiz-18

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. The probabilities that a student will obtain grades A,B,C or D are 0.30, 0.35, 0.20 and 0.15 respectively. The probability that he will receive atleast C grade, is
•  0.65
•  0.85
•  0.80
•  0.20
Solution

Q2. If X follows a binomial distribution with parameters n=100 and P=1/3, then P(X=r) is maximum when r is equal to
•  16
•  32
•  33
•  None of these
Solution

Q3. The probability that a teacher will give an unannounced test during any class meeting is 1/5. If a student is absent twice, the probability that he will miss atleast one test, is
• 7/25
•  9/25
•  16/25
•  24/25
Solution

Q4. Two dice are thrown together. If the numbers appearing on the two dice are different, then what is the probability that the sum is 6?
•  5/36
•  1/6
•  2/15
•  None of these
Solution

Q5. A binary operation is chosen at random from the set of all binary operations on a set A containing n elements. The probability that the binary operation is commutative, is
•  nn/n(n2)
•  n(n/2)/n(n2)
•  n(n/2)/(nn2/2)
•  None of these
Solution

Q6. The probability that a number selected at random from the set of numbers 1,2,3,4,…,100 is a cube, is
•  1/25
•  2/25
•  3/25
•  4/25
Solution

Q7. Two dice are rolled one after the other. The probability that the number on the first is smaller than the number on the second is
•  1/2
•  3/4
•  7/18
•  5/12
Solution

Q8. If P(A∩B) = 1/3, P(A∪B) = 5/6, and P(A)=1/2, then which one of the following is correct?
•  A and B are independent events
•  A and B are mutually exclusive events
•  P(A)=P(B)
•  None of the above

Solution

Q9. In an assembly of 4 persons the probability that at least 2 of them have the same birthday, is
•  0.293
•  0.24
•  0.0001
•  0.016
Solution

Q10. It is given the events A and B are such that P(A) = 1/4, P(A│B) = 1/2 and P(B│A) = 2/3. Then, P(B) is
•  1/2
•  1/6
•  1/3
•  2/3
Solution

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