Advertisements
Advertisements
प्रश्न
In eight throws of a die, 5 or 6 is considered a success. Find the mean number of successes and the standard deviation.
उत्तर
Let X denote the number of successes in 8 throws.
n =8
p = probability of getting 5 or 6 =
\[\frac{2}{6} = \frac{1}{3} \text{ and } q = \frac{2}{3}\]
\[\text{ Mean } (np) = \frac{8}{3}\]
\[\text{ Variance } (npq) = \frac{16}{9}\]
\[\text{ Standard deviation } = \sqrt{\text{ Variance} } = \frac{4}{3}\]
\[\text{ So, mean = 2 . 66 and standard deviation } = 1 . 33\]
APPEARS IN
संबंधित प्रश्न
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. What is the probability that out of 5 such bulbs
(i) none
(ii) not more than one
(iii) more than one
(iv) at least one, will fuse after 150 days of use.
It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?
Suppose that 90% of people are right-handed. What is the probability that at most 6 of a random sample of 10 people are right-handed?
The probability that a student is not a swimmer is 1/5 . Then the probability that out of five students, four are swimmers is
(A) `""^5C_4 (4/5)^4 1/5`
(B) `(4/5)^4 1/5
(C) `""^5C_1 1/5 (4/5)^4 `
(D) None of these
An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes.
A fair coin is tossed 8 times. Find the probability that it shows heads exactly 5 times.
If getting 5 or 6 in a throw of an unbiased die is a success and the random variable X denotes the number of successes in six throws of the die, find P (X ≥ 4).
Eight coins are thrown simultaneously. Find the chance of obtaining at least six heads.
A box contains 100 tickets, each bearing one of the numbers from 1 to 100. If 5 tickets are drawn successively with replacement from the box, find the probability that all the tickets bear numbers divisible by 10.
An urn contains four white and three red balls. Find the probability distribution of the number of red balls in three draws with replacement from the urn.
Three cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the mean and variance of number of red cards.
An unbiased die is thrown twice. A success is getting a number greater than 4. Find the probability distribution of the number of successes.
A man wins a rupee for head and loses a rupee for tail when a coin is tossed. Suppose that he tosses once and quits if he wins but tries once more if he loses on the first toss. Find the probability distribution of the number of rupees the man wins.
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 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 .
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 at least 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 .
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90% ?
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.
Can the mean of a binomial distribution be less than its variance?
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.
A die is tossed twice. A 'success' is getting an even number on a toss. Find the variance of number of successes.
The mean of a binomial distribution is 10 and its standard deviation is 2; write the value of q.
An unbiased coin is tossed 4 times. Find the mean and variance of the number of heads obtained.
If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3), then find the value of p.
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
In a binomial distribution, the probability of getting success is 1/4 and standard deviation is 3. Then, its mean is
Find the mean and variance of the random variable X which denotes the number of doublets in four throws of a pair of dice.
One of the condition of Bernoulli trials is that the trials are independent of each other.
Explain why the experiment of tossing a coin three times is said to have binomial distribution.
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 ______.
The mean, median and mode for binomial distribution will be equal when
If the coefficients of x7 and x8 in `(2 + x/3)^n` are equal, then n is
A fair coin is tossed 6 times. Find the probability of getting heads 4 times.
