Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KVPY2017MathematicsProbability

A shooter can hit a given target with probability 1 4 . She keeps firing a bullet at the target until she hits it successfully three times and then she stops firing. The probability that she fires exactly six bullets lies in the interval

Options

  1. A(0.5272,0.5274)
  2. B(0.2636,0.2638)
  3. C(0.1317,0.1319)
  4. D(0.0658,0.0660)

Correct answer

D. (0.0658,0.0660)

Step-by-step solution

3^ rd time target will hit in sixth time So, In first 5 attempt these will be 3 ~L , 2 ~W and at 6^ th attempt shot will be hit So, ⁵ C ₃ ( 3 4 )³ ( 1 4 )² ( 1 4 )= 270 4096 =0.06591

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