Probability-Quiz-13

Probability Quiz-13

Dear Readers,

Probability is an important topic in JEE advanced examination. In this exam, probability carries weightage of 7% of questions. With focused practice good marks can be fetched from this topic .

Q1. A class consists of 80 students, 25 of them are girls and 55 are boys. If 10 of them are rich and the remaining are poor and also 20 of them are intelligent, then the probability of selecting an intelligent rich girl is:

•  5/128
•  25/128
•  5/512
•  None of these

Solution

Q2. Three critics review a book. Odds in favour of the book are 5:2, 4:3 and 3:4, respectively, for the three cities. The probability that majority are in favour of the book is:

•  35/49
•  125/343
•  164/343
•  209/343

Solution

Q3.  A bag contains n white and n black balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each pair consists of one white and one black ball is:

•  1/²ⁿc_n
•  2n/²ⁿc_n
•  2n/n!
•  2n/2n!

Solution

Q4. Consider f(x)=x³+ax²+bx+c.Parameters a,b,c are chosen, respectively, by throwing a die throwing a die three times. Then the probability that f(x) is an increasing function is:

•  5/36
•  8/36
•  4/9
•  1/3

Solution

Q5. Dialing a telephone number an old man forgets the last two digits remembering only that these are different dialed at random. The probability that the number is dialed correctly is:

•  1/45
•  1/90
•  1/100
•  None of these

Solution

Q6. A bag contains some white and some black balls, all combinations of balls being equally likely. The total number of balls in the bag is 10. If three balls are drawn at random without replacement and all of them are found to be black, the probability that the bag contains 1 white and 9 black balls is:

•  14/55
•  12/55
• 2/11
•  8/55

Solution

Q7. A student can solve 2 out of 4 problem of mathematics, 3 out of 5problem of physics and 4 out of 5 problems of chemistry. There are equal number of books of math, physics and chemistry in his shelf. He selects one book randomly and attempts 10 problems from it. If he solves the first problem, then the probability that he will be able to solve the second problem is:

•  2/3
•  25/38
•  13/21
•  14/23

Solution

Q8.There are 20 cards. Ten of these cards have the letter ‘l’ printed on them and the other 10 have the letter. ‘T’ printed on them. If three cards are picked up at random and kept in the same order, the probability of making word IIT is:

•  4/27
•  5/38
•  1/8
•  9/80

Solution

Q9.A natural number is chosen at random from the first 100 natural numbers. The probability that x+100/x>50 is:

•  1/10
•  11/50
•  11/30
•  None of these

Solution

Q10. A bag contains 3 red and 3 green balls and a person draws out 3 at random. He then drops 3 blue balls into the bag and again out 3 at random. The chance that the 3 later balls being all of different colours is:

•  15%
•  20%
•  27%
• 40%

Solution