Advertisements
Advertisements
Question
An unbiased die is thrown twice. A success is getting a number greater than 4. Find the probability distribution of the number of successes.
Solution
Let X denote getting a number greater than 4 .
Then, X follows a binomial distribution with n=2
\[p = P(X > 4) = P(X = 5 \text{ or } 6)\]
\[ = \frac{1}{6} + \frac{1}{6}\]
\[ = \frac{1}{3}\]
\[q = 1 - p = \frac{2}{3}\]
\[P(X = r) = ^ {2}{}{C}_r \left( \frac{1}{3} \right)^r \left( \frac{2}{3} \right)^{2 - r} , r = 0, 1, 2 \]
\[\text{ Substituting for r we get probability distribution of X as follows } .\]
X 0 1 2
\[P(X) \frac{4}{9} \frac{4}{9} \frac{1}{9}\]
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.
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
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?
Five cards are drawn one by one, with replacement, from a well-shuffled deck of 52 cards. Find the probability that
(i) all the five cards diamonds
(ii) only 3 cards are diamonds
(iii) none is a diamond
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?
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 coin is tossed 8 times. Find, by using binomial distribution, the probability of getting at least 6 heads.
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 .
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.
The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university all 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.
How many times must a man toss a fair coin so that the probability of having at least one head is more than 80% ?
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.
A factory produces bulbs. The probability that one bulb is defective is \[\frac{1}{50}\] and they are packed in boxes of 10. From a single box, find the probability that none of the bulbs is defective .
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 and variance of a binomial variate with parameters n and p are 16 and 8, respectively. Find P (X = 0), P (X = 1) and P (X ≥ 2).
A dice is thrown thrice. A success is 1 or 6 in a throw. Find the mean and variance of the number of successes.
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.
A die is thrown three times. Let X be 'the number of twos seen'. Find the expectation of X.
In a binomial distribution, if n = 20 and q = 0.75, then write its mean.
If the mean of a binomial distribution is 20 and its standard deviation is 4, find p.
In a box containing 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs, none is defective?
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
One hundred identical coins, each with probability p of showing heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of p is
A fair coin is tossed 99 times. If X is the number of times head appears, then P (X = r) is maximum when r is
A coin is tossed 10 times. The probability of getting exactly six heads is
In a binomial distribution, the probability of getting success is 1/4 and standard deviation is 3. Then, its mean is
Mark the correct alternative in the following question:
A box contains 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?
Bernoulli distribution is a particular case of binomial distribution if n = ______
One of the condition of Bernoulli trials is that the trials are independent of each other.
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 ______.
