Advertisements
Advertisements
Question
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.
Solution
\[\text{ Let X denote the number of machines out of service during a day . } \]
\[\text{ Then, X follows a binomial distribution with n = 20 } \]
\[\text{ Let p be the probability of any machine out of service during a day } . \]
\[ \therefore p = 0 . 02 \text{ and } q = 0 . 98 \]
\[\text{ Hence, the distribution is given by } \]
\[P(X = r) = ^{20}{}{C}_r \left( 0 . 02 \right)^r \left( 0 . 98 \right)^{20 - r} , r = 0, 1, 2 . . . . . 20\]
\[ \therefore P(\text{ exactlly 3 machines will be out of the service on the same day } ) = P(X = 3)\]
\[ = ^{20}{}{C}_3 \left( 0 . 02 \right)^3 \left( 0 . 98 \right)^{20 - 3} \]
\[ = 1140(0 . 000008)(0 . 7093)\]
\[ = 0 . 006469\]
APPEARS IN
RELATED QUESTIONS
A couple has two children, Find the probability that both children are females, if it is known that the elder child is a female.
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?
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.
A coin is tossed 5 times. If X is the number of heads observed, find the probability distribution of X.
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
\[\frac{28 \times 9^6}{{10}^8} .\]
Suppose that a radio tube inserted into a certain type of set has probability 0.2 of functioning more than 500 hours. If we test 4 tubes at random what is the probability that exactly three of these tubes function for more than 500 hours?
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 .
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 none contract the disease .
The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university only one will graduate .
Ten eggs are drawn successively, with replacement, from a lot containing 10% defective eggs. Find the probability that there is at least one defective egg.
Suppose X has a binomial distribution with n = 6 and \[p = \frac{1}{2} .\] Show that X = 3 is the most likely outcome.
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of the number of successes.
If the mean and variance of a binomial distribution are respectively 9 and 6, find the distribution.
In a binomial distribution the sum and product of the mean and the variance are \[\frac{25}{3}\] and \[\frac{50}{3}\]
respectively. Find the distribution.
The mean of a binomial distribution is 20 and the standard deviation 4. Calculate the parameters of the binomial distribution.
Find the expected number of boys in a family with 8 children, assuming the sex distribution to be equally probable.
If a random variable X follows a binomial distribution with mean 3 and variance 3/2, find P (X ≤ 5).
If the sum of the mean and variance of a binomial distribution for 6 trials is \[\frac{10}{3},\] find the distribution.
In a binomial distribution, if n = 20 and q = 0.75, then write its mean.
If the mean and variance of a binomial variate X are 2 and 1 respectively, find P (X > 1).
If for a binomial distribution P (X = 1) = P (X = 2) = α, write P (X = 4) in terms of α.
Fifteen coupons are numbered 1 to 15. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9 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
A coin is tossed n times. The probability of getting at least once is greater than 0.8. Then, the least value of n, is
Mark the correct alternative in the following question:
Suppose a random variable X follows the binomial distribution with parameters n and p, where 0 < p < 1. If \[\frac{P\left( X = r \right)}{P\left( X = n - r \right)}\] is independent of n and r, then p equals
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 any two are white ?
For Bernoulli Distribution, state formula for E(X) and V(X).
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
Suppose a random variable X follows the binomial distribution with parameters n and p, where 0 < p < 1. If P(x = r)/P(x = n – r) is independent of n and r, then p equals ______.
In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is:-
The mean and variance of a binomial distribution are α and `α/3` respectively. If P(X = 1) = `4/243`, then P(X = 4 or 5) is equal to ______.
A fair coin is tossed 6 times. Find the probability of getting heads 4 times.
If the sum of mean and variance of a binomial distribution is `25/9` for 5 trials, find p.
