Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let X = number of winning prizes.
p = probability of winning a prize
∴ p = `1/100`
and q = 1 − p = 1 − `1/100` = `99/100`
Given: n = 50
∴ X ~ B `(50, 1/100)`
The p.m.f. of X is given by P(X = x) = `""^nC_x p^x q^(n - x)`
i.e. p(x) = `""^50C_x (1/100)^x(99/100)^(50-x), x = 0, 1, 2, ...50`
P(a person wins a prize at least once)
= P[X ≥ 1] = 1 − P[X < 1] = 1 − p(0)
= 1 − `""^50C_0 (1/100)^0 (99/100)^(50-0)`
= 1 − 1 × 1 × `(99/100)^50`
= 1 − `(99/100)^50`
Hence, probability of winning a prize at least once
= 1 − `(99/100)^50`
APPEARS IN
संबंधित प्रश्न
A fair coin is tossed 8 times. Find the probability that it shows heads at least once
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.
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.
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.
In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is 5/6 . What is the probability that he will knock down fewer than 2 hurdles?
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.
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
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 ?
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?
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?
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?
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 at most 3 will survive .
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 .
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 .
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 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.
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.
A die is thrown three times. Let X be 'the number of twos seen'. Find the expectation of X.
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 X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3), then find the value of p.
A fair coin is tossed a fixed number of times. If the probability of getting seven heads is equal to that of getting nine heads, the probability of getting two heads 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 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
In a binomial distribution, the probability of getting success is 1/4 and standard deviation is 3. Then, its mean 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 at least 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.
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.
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 ______.
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.
If X ∼ B(n, p), n = 6 and 9 P(X = 4) = P(X = 2), then find the value of p.
