Probability Quiz-17

Probability Quiz-17 

Dear Readers,

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. An insurance salesman sells policies to 5 men, all of identical age and in good health. The probability that a man of this particular age will be alive after 30 years is 2/3. The probability that after the lapse of 30 years all the five persons will be alive, is

•  1/16
•  16/81
•  32/243
•  None of these

Solution

Q2. Out of 40 consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is

•  14/29
•  20/39
•  1/2
•  None of these

Solution

Q3. A fair coin is tossed a fixed number of times. If the probability of getting 4 heads equals the probability of getting 7 heads, then the probability of getting 2 heads is

• 55/2048
•  3/4096
•  1/1024
•  None of these

Solution

Q4. If two events A and B are such that P(A^c )=0.3, P(B)=0.4, P(A∩B^c)=0.5, then P(B/A∪B^c) =

•  0.20
•  0.25
•  0.30
•  0.35

Solution

Q5. A six faced die is a biased one. It is thrice more likely to show an odd number than show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even, is

•  5/9
  
•  5/8
•  1/2
•  None of these

Solution

Q6. To open a lock, a key is taken out from a collection of n keys at random. If the lock is not opened with this key, it is put back into the collection and another key is tried. The process is repeated again and again. If it is given that with only one key in the collection, the lock can be opened, then the probability that the lock will open in n trials, is

•  (1/n)ⁿ
•  ((n-1)/n)ⁿ
•  1-((n-1)/n)ⁿ
•  None of these

Solution

Q7. If n positive integers are taken at random and multiplied together, the probability that the last digit of the product is 2, 4, 6 or 8, is

•  (4ⁿ+2ⁿ)/5ⁿ
•  (4ⁿ×2ⁿ)/5ⁿ
•  (4ⁿ-2ⁿ)/5ⁿ
•  None of these

Solution

Q8. A bag contains 5 white and 3 black balls and 4 balls are successively drawn out and not replaced. The probability that they are alternately of different colours, is

•  1/196
•  2/7
•  13/56
•  1/7

Solution

Q9. The odds against a certain event are 5 : 2 and the odds in favour of another independent event are 6 : 5. The probability that at least one of the events will happen, is

•  25/77
•  52/77
•  12/77
•  65/77

Solution

Q10. If a dice is thrown twice, the probability of occurrence of 4 at least once is

•  11/36
•  35/36
•  7/12
•  None of these

Solution