Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KVPY2016MathematicsProbability

If a 3-digit number is randomly chosen, what is the probability that either the number itself or some permutation of the number (which is a 3 -digit number) is divisible by 4 and 5 ?

Options

  1. A1 45
  2. B29 180
  3. C11 60
  4. D1 4

Correct answer

B. 29 180

Step-by-step solution

We need 3 -digit number which is divisible by 4 & 5 both. i.e. their last two digits are 00,20,40,60 & 80 Now, ending with 00 are '9'. 100,200, , 900 If digit repeat other than ' 0 ' then they are 220,440,660,880 but 220 numbers can be permuted according to the condition as 220,202 So, there are ' 8 ' other favorable cases. If the number have no digit repeated like 320 . 320 can be permuted in 4 ways. 302,230,320,203 So, such numbers are 8 4 4=128 Total favorable =9+8+128=145 So, required prob. = 145 900 = 29 180

Practice Probability on Quantrex Academy →

More from Probability

Two students appeared simultaneously for an entrance exam. If the probability that the first student gets qualified in the exam is 1 4 and the probability that the second student g 2025For three events A, B and C of a sample space, P(exactly one of A or B occurs)= P ( exactly one of B or C occurs )= P ( exactly one of C or A occurs )= 1 4 . If probability of all 2025A bag P contains 4 red and 5 black balls, another bag Q contains 3 red and 6 black balls. If one ball is drawn at random from bag P and two balls are drawn from bag Q, then the pro 2025On every evening, a student either watches TV or reads a book. The probability of watching TV is 4 5 . If he watches TV, the probability that he will fall asleep is 3 4 and it is 1 2025Let X be the random variable taking values 1,2, , n for a fixed positive integer n. If P ( X = k )= 1 n for 1 k n , then the variance of X is 2025A radar system can detect an enemy plane in one out of ten consecutive scans. The probability that it can detect an enemy plane atleast twice in four consecutive scans is 2025Three numbers are chosen from 1 to 30. The probability that they are not three consecutive numbers is 2025If two events A and B are such that P ( A )=0.3, P ( B )=0.4 and P ( A B )=0.5 , then P ( B /( A B ))= 2025 Full Probability list All KVPY PYQs