Advertisements
Advertisements
प्रश्न
An unbiased coin is tossed 8 times. Find, by using binomial distribution, the probability of getting at least 6 heads.
उत्तर
Let X be the number of heads in tossing the coin 8 times.
X follows a binomial distribution with n = 8
\[p = \frac{1}{2} \text{ and q } = \frac{1}{2}\]
\[\text{ Hence, the distribution is given by } \]
\[ \therefore P(X = r) = ^{8}{}{C}_r \left( \frac{1}{2} \right)^r \left( \frac{1}{2} \right)^{8 - r} , r = 0, 1, 2, 3, 4, 5, 6, 7, 8\]
\[\text{ Required probability } = P(X \geq 6)\]
\[ = P(X = 6) + P(X = 7) + P(X = 8)\]
\[ = \frac{^{8}{}{C}_6 + ^{8}{}{C}_7 + ^{8}{}{C}_8}{2^8}\]
\[ = \frac{28 + 8 + 1}{256}\]
\[ = \frac{37}{256}\]
APPEARS IN
संबंधित प्रश्न
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.
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?
Find the probability of getting 5 exactly twice in 7 throws of a die.
In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is
(A) 10−1
(B) `(1/2)^5`
(C) `(9/10)^5`
(D) 9/10
A couple has two children, Find the probability that both children are males, if it is known that at least one of the children is male.
A couple has two children, Find the probability that both children are females, if it is known that the elder child is a female.
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?
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.
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.
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?
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
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 .
A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is \[\frac{1}{100} .\] What is the probability that he will win a prize exactly once.
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.
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.
The probability of a man hitting a target is 0.25. He shoots 7 times. What is the probability of his hitting at least twice?
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.
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.
Find the binomial distribution whose mean is 5 and variance \[\frac{10}{3} .\]
If the mean and variance of a random variable X with a binomial distribution are 4 and 2 respectively, find P (X = 1).
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
The least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8, is
If X follows a binomial distribution with parameters n = 100 and p = 1/3, then P (X = r) is maximum when r =
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
Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that only 3 cards are spades ?
Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that none is a spade ?
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
Bernoulli distribution is a particular case of binomial distribution if n = ______
If a fair coin is tossed 10 times. Find the probability of getting at most six heads.
If X ∼ B(n, p), n = 6 and 9 P(X = 4) = P(X = 2), then find the value of p.
