Advertisements
Advertisements
प्रश्न
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.
उत्तर
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
संबंधित प्रश्न
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?
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that
- all the five cards are spades?
- only 3 cards are spades?
- none is a spade?
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.
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 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.
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
A fair coin is tossed 8 times. Find the probability that it shows heads exactly 5 times.
A fair coin is tossed 9 times. Find the probability that it shows head exactly 5 times.
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
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).
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 ?
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?
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?
Find the probability distribution of the number of doublets in 4 throws of a pair of dice.
A coin is tossed 5 times. If X is the number of heads observed, find the probability distribution of X.
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 mathematics department has 8 graduate assistants who are assigned to the same office. Each assistant is just as likely to study at home as in office. How many desks must there be in the office so that each assistant has a desk at least 90% of the time?
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
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.
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 none will graduate
In a multiple-choice examination with three possible answers for each of the five questions out of which only one is correct, what is the probability that a candidate would get four or more correct answers just by guessing?
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.
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
A box has 20 pens of which 2 are defective. Calculate the probability that out of 5 pens drawn one by one with replacement, at most 2 are defective.
Can the mean of a binomial distribution be less than its variance?
Determine the binomial distribution whose mean is 20 and variance 16.
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.
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.
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).
The probability that an item produced by a factory is defective is 0.02. A shipment of 10,000 items is sent to its warehouse. Find the expected number of defective items and the standard deviation.
A dice is thrown thrice. A success is 1 or 6 in a throw. Find the mean and variance of the number of successes.
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 the mean and variance of a binomial variate X are 2 and 1 respectively, find P (X > 1).
If in a binomial distribution n = 4 and P (X = 0) = \[\frac{16}{81}\] , find q.
If the mean and variance of a binomial distribution are 4 and 3, respectively, find the probability of no success.
If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3), then find the value of 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?
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
If the mean and variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than 1 is
A biased coin with probability p, 0 < p < 1, of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is 2/5, then p equals
If X follows a binomial distribution with parameters n = 8 and p = 1/2, then P (|X − 4| ≤ 2) equals
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 coin is tossed 4 times. The probability that at least one head turns up is
For a binomial variate X, if n = 3 and P (X = 1) = 8 P (X = 3), then p =
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:
The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is
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 not more than one will fuse after 150 days of use
Find the mean and variance of the random variable X which denotes the number of doublets in four throws of a pair of dice.
For Bernoulli Distribution, state formula for E(X) and V(X).
The mean, median and mode for binomial distribution will be equal when
If x4 occurs in the tth term in the expansion of `(x^4 + 1/x^3)^15`, then the value oft is equal to:
If a fair coin is tossed 10 times. Find the probability of getting at most six heads.
If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then `(P(X = 2))/(P(X = 3))` is equal to ______.
If a random variable X follows the Binomial distribution B (33, p) such that 3P(X = 0) = P(X = 1), then the value of `(P(X = 15))/(P(X = 18)) - (P(X = 16))/(P(X = 17))` 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.
In three throws with a pair of dice find the chance of throwing doublets at least twice.
If X ∼ B(n, p), n = 6 and 9 P(X = 4) = P(X = 2), then find the value of p.
The mean and variance of binomial distribution are 4 and 2 respectively. Find the probability of two successes.
