Advertisements
Advertisements
Question
The probability that a bomb will hit a target is 0.8. Find the probability that out of 10 bombs dropped, exactly 4 will hit the target.
Solution
Let r = no of bombs hit the target
p=0.8
q=0.2 (1-p=q)
n=10 r=4
`p(r=4)=""^nC_rp^rq^(n-r)` r=0,1,2...........,n
`=""^10C_4(0.8)^4(0.2)^6`
`=""^10C_4(8/10)^4(2/10)^6`
`=(10!)/(4!6!) xx(2)^18(1/10)^10`
`=(10xx9xx8xx7)/(4xx3xx2)xx(2)^18xx(1/10)^10`
`=210xx(2)^18xx(1/10)^10`
`=(262144xx210)/(10)^10=55050240/(10)^10`
`=Anti[log210+18log2-10]`
`=Anti[2.3222+18log(0.3010)-10]`
`=Anti(3.7402)`
`=0.0055`
APPEARS IN
RELATED QUESTIONS
Given that X ~ B(n= 10, p). If E(X) = 8 then the value of
p is ...........
(a) 0.6
(b) 0.7
(c) 0.8
(d) 0.4
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.
There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?
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?
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.
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)
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?
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 in a prize (a) at least once (b) exactly once (c) at least twice?
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?
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.
Assume that on an average one telephone number out of 15 called between 2 P.M. and 3 P.M. on week days is busy. What is the probability that if six randomly selected telephone numbers are called, at least 3 of them will be busy?
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.
Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that all the five cards are spades ?
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
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.
An unbiased die is thrown twice. A success is getting a number greater than 4. Find the probability distribution of the number of successes.
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.
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?
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 .
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.
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 \[\frac{1}{100} .\] What is the probability that he will win a prize exactly 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 at least twice.
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?
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90% ?
How many times must a man toss a fair coin so that the probability of having at least one head is more than 80% ?
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.
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.
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 exactly two bulbs are defective
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 more than 8 bulbs work properly
If the mean and variance of a binomial distribution are respectively 9 and 6, find the distribution.
Find the binomial distribution when the sum of its mean and variance for 5 trials is 4.8.
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 on an average 9 ships out of 10 arrive safely at ports, find the mean and S.D. of the ships returning safely out of a total of 500 ships.
If a random variable X follows a binomial distribution with mean 3 and variance 3/2, find P (X ≤ 5).
The mean and variance of a binomial distribution are \[\frac{4}{3}\] and \[\frac{8}{9}\] respectively. Find P (X ≥ 1).
In a binomial distribution, if n = 20 and q = 0.75, then write its mean.
If in a binomial distribution mean is 5 and variance is 4, write the number of trials.
The mean of a binomial distribution is 10 and its standard deviation is 2; write the value of q.
If for a binomial distribution P (X = 1) = P (X = 2) = α, write P (X = 4) in terms of α.
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
A fair coin is tossed 100 times. The probability of getting tails an odd number of times is
A fair die is thrown twenty times. The probability that on the tenth throw the fourth six appears is
If X follows a binomial distribution with parameters n = 8 and p = 1/2, then P (|X − 4| ≤ 2) equals
If X follows a binomial distribution with parameters n = 100 and p = 1/3, then P (X = r) is maximum when r =
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
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
A coin is tossed 10 times. The probability of getting exactly six heads is
If the mean and variance of a binomial distribution are 4 and 3, respectively, the probability of getting exactly six successes in this distribution 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
The probability of selecting a male or a female is same. If the probability that in an office of n persons (n − 1) males being selected is \[\frac{3}{2^{10}}\] , the 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 ?
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
If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9, P(X = 3), then p = ______.
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 ______.
The probability of hitting a target in any shot is 0.2. If 5 shots are fired, find the probability that the target will be hit at least twice.
If X ∼ B(n, p), n = 6 and 9 P(X = 4) = P(X = 2), then find the value of p.
An experiment succeeds thrice as often as it fails. Then in next five trials, find the probability that there will be two successes.
For the binomial distribution X ∼ B(n, p), n = 6 and P(X = 4) = P(X = 2). find p.
