Advertisements
Advertisements
प्रश्न
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs at least one will fuse after 150 days of use
उत्तर
Let X be the number of bulbs that fuse after 150 days.
X follows a binomial distribution with n = 5,
\[\text{ Or } p = \frac{1}{20}\text{ and } q = \frac{19}{20}\]
\[P(X = r) = ^{5}{}{C}_r \left( \frac{1}{20} \right)^r \left( \frac{19}{20} \right)^{5 - r} \]
\[ \text{ Probability } \left( \text{ at least one will fuse after 150 days of use } \right) = P(X \geq 1)\]
\[ = 1 - P(X = 0) \]
\[ = 1 - \left( \frac{19}{20} \right)^5 \left\{ \because P(X = 0 = \left( \frac{19}{20} \right)^5 \right\}\]
APPEARS IN
संबंधित प्रश्न
There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?
In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers ‘true’; if it falls tails, he answers ‘false’. Find the probability that he answers at least 12 questions correctly.
On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?
Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that all the five cards are spades ?
A bag contains 10 balls, each marked with one of the digits from 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs none will fuse after 150 days of use
A bag contains 7 green, 4 white and 5 red balls. If four balls are drawn one by one with replacement, what is the probability that one is red?
A bag contains 2 white, 3 red and 4 blue balls. Two balls are drawn at random from the bag. If X denotes the number of white balls among the two balls drawn, describe the probability distribution of X.
Find the probability distribution of the number of sixes in three tosses of a die.
Five dice are thrown simultaneously. If the occurrence of 3, 4 or 5 in a single die is considered a success, find the probability of at least 3 successes.
The items produced by a company contain 10% defective items. Show that the probability of getting 2 defective items in a sample of 8 items is
\[\frac{28 \times 9^6}{{10}^8} .\]
The probability that a certain kind of component will survive a given shock test is \[\frac{3}{4} .\] Find the probability that among 5 components tested exactly 2 will survive .
Assume that the probability that a bomb dropped from an aeroplane will strike a certain target is 0.2. If 6 bombs are dropped, find the probability that exactly 2 will strike the target .
It is known that 60% of mice inoculated with a serum are protected from a certain disease. If 5 mice are inoculated, find the probability that more than 3 contract the disease .
An experiment succeeds twice as often as it fails. Find the probability that in the next 6 trials there will be at least 4 successes.
In a hospital, there are 20 kidney dialysis machines and the chance of any one of them to be out of service during a day is 0.02. Determine the probability that exactly 3 machines will be out of service on the same day.
The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university none will graduate
From a lot of 30 bulbs that includes 6 defective bulbs, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.
If the mean and variance of a binomial distribution are respectively 9 and 6, find the distribution.
The mean of a binomial distribution is 20 and the standard deviation 4. Calculate the parameters of the binomial distribution.
If the probability of a defective bolt is 0.1, find the (i) mean and (ii) standard deviation for the distribution of bolts in a total of 400 bolts.
If the sum of the mean and variance of a binomial distribution for 6 trials is \[\frac{10}{3},\] find the distribution.
A rifleman is firing at a distant target and has only 10% chance of hitting it. The least number of rounds he must fire in order to have more than 50% chance of hitting it at least once is
If X is a binomial variate with parameters n and p, where 0 < p < 1 such that \[\frac{P\left( X = r \right)}{P\left( X = n - r \right)}\text{ is } \] independent of n and r, then p equals
Let X denote the number of times heads occur in n tosses of a fair coin. If P (X = 4), P (X= 5) and P (X = 6) are in AP, the value of n is
A fair die is tossed eight times. The probability that a third six is observed in the eighth throw is
A five-digit number is written down at random. The probability that the number is divisible by 5, and no two consecutive digits are identical, is
In a binomial distribution, the probability of getting success is 1/4 and standard deviation is 3. Then, its mean is
A coin is tossed 4 times. The probability that at least one head turns up is
Mark the correct alternative in the following question:
Which one is not a requirement of a binomial dstribution?
A bag contains 7 red, 5 white and 8 black balls. If four balls are drawn one by one with replacement, what is the probability that all are white ?
Determine the binomial distribution where mean is 9 and standard deviation is `3/2` Also, find the probability of obtaining at most one success.
For X ~ B(n, p) and P(X = x) = `""^8"C"_x(1/2)^x (1/2)^(8 - x)`, then state value of n and p
If x4 occurs in the tth term in the expansion of `(x^4 + 1/x^3)^15`, then the value oft is equal to:
A pair of dice is thrown four times. If getting a doublet is considered a success then find the probability of two success.
An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is ______.
If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then `(P(X = 2))/(P(X = 3))` is equal to ______.
