Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202522 Apr 2025Evening ShiftMathematicsProbabilityActual

Four defective oranges are accidentally mixed with sixteen good ones. Three oranges are drawn from the mixed lot. The probability distribution of defective oranges is

Options

  1. A( array |c|c|c|c|c| X & 0 & 1 & 2 & 3 P ( X =x) & 28 57 & 8 95 & 8 19 & 1 285 array )
  2. B( array |c|c|c|c|c| X & 0 & 1 & 2 & 3 P ( X =x) & 28 57 & 8 19 & 8 95 & 1 285 array )
  3. C( array |c|c|c|c|c| X & 0 & 1 & 2 & 3 P ( X =x) & 28 57 & 8 95 & 1 285 & 8 19 array )
  4. D( array |c|c|c|c|c| X & 0 & 1 & 2 & 3 P ( X =x) & 1 285 & 8 95 & 8 19 & 28 57 array )

Correct answer

B. ( array |c|c|c|c|c| X & 0 & 1 & 2 & 3 P ( X =x) & 28 57 & 8 19 & 8 95 & 1 285 array )

Step-by-step solution

The lot contains 4 defective and 16 good oranges, totaling 20 oranges. Let X represent the number of defective oranges when drawing 3 without replacement. The total number of ways to draw 3 oranges is 20 3 = 1140 . For X = 0 : Probability is 4 0 16 3 1140 = 1 560 1140 = 28 57 . For X = 1 : Probability is 4 1 16 2 1140 = 4 120 1140 = 8 19 . For X = 2 : Probability is 4 2 16 1 1140 = 6 16 1140 = 8 95 . For X = 3 : Probability is 4 3 16 0 1140 = 4 1 1140 = 1 285 . The probability distribution matches Option B .

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 MHT CET PYQs