From a lot containing 10 defective and 90 non-defective bulbs, 8...

From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is

Options

A $\frac{67}{10^{8}}$
B $\frac{7}{10^{7}}$
C $\frac{81}{10^{8}}$
D $\frac{73}{10^{8}}$

Correct answer

D. $\frac{73}{10^{8}}$

Step-by-step solution

Binomial distribution with

n=8

p=\frac{1}{10}

q=\frac{9}{10}

P(X \ge 7) = P(X=7) + P(X=8)

P(X=7) = \binom{8}{7}\left(\frac{1}{10}\right)^7\left(\frac{9}{10}\right) = \frac{72}{10^8}

P(X=8) = \left(\frac{1}{10}\right)^8 = \frac{1}{10^8}

P(X \ge 7) = \frac{73}{10^8}

Practice Probability on Quantrex Academy →

More from Probability

Suppose that Box I contains 6 red balls and 9 green balls, and Box II contains 8 red… JEE Advanced 2026 A candidate has to go to the examination centre to appear in an examination. The… JEE Main 2026 A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement… JEE Main 2026 A bag contains (N+1) coins - N fair coins, and one coin with 'Head' on both sides. A coin… JEE Main 2026 The probabilities that players A and B of a team are selected for the captaincy for a… JEE Main 2026 A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the… JEE Main 2026 From a month of 31 days, 3 different dates are selected at random. If the probability… JEE Main 2026 A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six… JEE Main 2026 A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5… JEE Main 2026 The probability distribution of a random variable X is given below : (array… JEE Main 2026 A bag contains 10 balls out of which k are red and ( 10-k ) are black, where 0 ≤ k ≤ 10 .… JEE Main 2026 Let S be a set of 5 elements and P(S) denote the power set of S. Let E be an event of… JEE Main 2026 Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls.… JEE Main 2026 From the first 100 natural numbers, two numbers first a and then b are selected randomly… JEE Main 2026 If a random variable x has the probability distribution array |c|c|c|c|c|c|c|c|c| x & 0 &… JEE Main 2026 Two distinct numbers a and b are selected at random from 1,2,3, …, 50 . The probability… JEE Main 2026 Full Probability list Probability JEE Maths PYQs JEE Mathematics PYQs All JEE Main PYQs