## Probability Quiz-12

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. One hundred identical coins, each with probability p or showing up heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of  is
•  1/2
•  49/101
•  50/101
•  51/101
Solution

Q2. Three six faced dice are tossed together, then the probability that exactly two of the three numbers are equal is
•  165/216
•  177/216
•  51/216
•  90/216
Solution

Q3. Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse, is
• 4/5
•  3/5
•  1/5
•  2/5
Solution

Q4. If If in a trial the probability of success is twice the probability of failure. In six trials the probability of at least four successes is
•  496/729
•  400/729
•  500/729
•  600/729
Solution

Q5. If A and B are events of the same experiments with P(A)=0.2,P(B)=0.5 ,then maximum value of P(A'∩B) is
•  0.2
•  0.5
•  0.63
•  0.25
Solution

Q6. A coin is tossed three times. The probability of getting a head once and a tail twice is
•  1/8
•  1/3
•  3/8
•  1/2
Solution

Q7. Out of 3n consecutive natural numbers, 3 natural numbers are chosen at random without replacement. The probability that the sum of the chosen numbers is divisible by 3, is
•  (n(3n2-3n+2))/2
•  ((3n2-3n+2))/(2(3n-1)(3n-2))
•  ((3n2-3n+2))/((3n-1)(3n-2))
•  (n(3n-1)(3n-2))/(3(n-1))

Solution

Q8. If A and B are two events than the value of the determinant choosen at random from all the determinants of order 2 with entries 0 or 1 only is positive or negative respectively. Then,
•  P(A) > P(B)
•  P(A) < P(B)
•  P(A) = P(B) = 1/2
•  P(A) = P(B)

Solution

Q9. A man is known to speak truth in 75% cases. If he throws an unbiased die and tells his friend that it is a six, then the probability that it is actually a six, is
•  1/6
•  1/8
•  3/4
•  3/8
Solution

Q10. Suppose that a die (with faces marked 1 to 6) is loaded in such a manner that for K=1,2,3,….,6 the probability of the face marked K turning up when die is tossed is proportional to K. The probability of the event that the outcome of a toss of the die will be an even number, is equal to
•  1/2
•  4/7
•  2/5
•  1/21
Solution

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