Advertisements
Advertisements
प्रश्न
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.
उत्तर
Let X represent the number of correctly answered questions out of 20 questions.
The repeated tosses of a coin are Bernoulli trails. Since “head” on a coin represents the true answer and “tail” represents the false answer, the correctly answered questions are Bernoulli trials.
`:. p = 1/2`
`:. q =1 - p = 1-1/2 = 1/2`
X has a binomial distribution with n = 20 and p = 1/2
APPEARS IN
संबंधित प्रश्न
Given X ~ B (n, p)
If n = 10 and p = 0.4, find E(X) and var (X).
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.
A bag consists of 10 balls each marked with one of the digits 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?
Suppose X has a binomial distribution `B(6, 1/2)`. Show that X = 3 is the most likely outcome.
(Hint: P(X = 3) is the maximum among all P (xi), xi = 0, 1, 2, 3, 4, 5, 6)
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.
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.
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.
Find the probability distribution of the number of sixes in three tosses of a die.
An unbiased die is thrown twice. A success is getting a number greater than 4. Find the probability distribution of the number of 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
\[\frac{28 \times 9^6}{{10}^8} .\]
A card is drawn and replaced in an ordinary pack of 52 cards. How many times must a card be drawn so that (i) there is at least an even chance of drawing a heart (ii) the probability of drawing a heart is greater than 3/4?
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 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 .
In a 20-question true-false examination, suppose a student tosses a fair coin to determine his answer to each question. For every head, he answers 'true' and for every tail, he answers 'false'. Find the probability that he answers at least 12 questions correctly.
Suppose X has a binomial distribution with n = 6 and \[p = \frac{1}{2} .\] Show that X = 3 is the most likely outcome.
A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is `1/100`. What is the probability that he will win a prize at least once.
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.
The probability of a shooter hitting a target is \[\frac{3}{4} .\] How many minimum number of times must he/she fire so that the probability of hitting the target at least once is more than 0.99?
Find the probability that in 10 throws of a fair die, a score which is a multiple of 3 will be obtained in at least 8 of the throws.
If the mean and variance of a binomial distribution are respectively 9 and 6, 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).
If X follows a binomial distribution with mean 4 and variance 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.
If the mean of a binomial distribution is 20 and its standard deviation is 4, find p.
A fair die is thrown twenty times. The probability that on the tenth throw the fourth six appears 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
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
If X follows a binomial distribution with parameters n = 100 and p = 1/3, then P (X = r) is maximum when r =
A fair die is tossed eight times. The probability that a third six is observed in the eighth throw 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 ?
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 more than one will fuse after 150 days of use
Bernoulli distribution is a particular case of binomial distribution if n = ______
The mean, median and mode for binomial distribution will be equal when
In three throws with a pair of dice find the chance of throwing doublets at least twice.
A fair coin is tossed 8 times. Find the probability that it shows heads at most once.
