From a lot containing 10 defective and 90 non | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Total bulbs = $100$. Number of defective bulbs = $10$. Number of non-defective bulbs = $90$.Probability of selecting a defective bulb $p = \frac{1

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) Total bulbs = $100$. Number of defective bulbs = $10$. Number of non-defective bulbs = $90$.Probability of selecting a defective bulb $p = \frac{10}{100} = \frac{1}{10}$.Probability of selecting a non-defective bulb $q = \frac{90}{100} = \frac{9}{10}$.Since bulbs are selected with replacement, this follows a Binomial Distribution $B(n, p)$ with $n = 8$ and $p = 0.1$.The probability of getting at least $7$ defective bulbs is $P(X \ge 7) = P(X = 7) + P(X = 8)$.$P(X = 7) = \binom{8}{7} 	imes (0.1)^7 	imes (0.9)^1 = 8 	imes \frac{1}{10^7} 	imes \frac{9}{10} = \frac{72}{10^8}$.$P(X = 8) = \binom{8}{8} 	imes (0.1)^8 	imes (0.9)^0 = 1 	imes \frac{1}{10^8} 	imes 1 = \frac{1}{10^8}$.Total probability = $\frac{72}{10^8} + \frac{1}{10^8} = \frac{73}{10^8}$.

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:

Similar Questions

The probability of a person hitting a bird is $3/4$. If he tries $5$ times,what is the probability that he will not hit the bird even once (in $/1024$)?

If the mean and the variance of a binomial variate $X$ are $1$ and $0.75$ respectively, then which of the following is true?

For an initial screening of an entrance exam,a candidate is given $50$ problems to solve. If the probability that the candidate can solve any problem is $\frac{4}{5}$,then the probability that he is unable to solve less than $2$ problems is:

If $X$ and $Y$ are two independent binomial variates,satisfying $B(10, 1/2)$ and $B(8, 1/2)$ respectively,then the probability $P(X + Y = 2)$ is

The probability of an event $A$ happening in one trial is $0.4$. The probability that the event $A$ happens at least once in three independent trials is

Vedclass Test Series

Exam Paper Generator

Online Exam Module