Advertisements
Advertisements
प्रश्न
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.
उत्तर
Let X denote the number of white balls when 2 balls are drawn from the bag.
X follows a distribution with values 0,1 or 2.
\[P(X = 0) = P(\text{ All balls non - white } ) = \frac{^{7}{}{C}_2}{^{9}{}{C}_2} = \frac{42}{72} = \frac{21}{36}\]
\[P(X = 1) = P \hspace{0.167em} ( Ist \hspace{0.167em}\text{ ball white and IInd ball non - white } ) \hspace{0.167em} \]
\[ = \frac{^{7}{}{C}_1 ^{2}{}{C}_1}{^{9}{}{C}_2} = \frac{14}{36}\]
\[P(X = 2) = P( \text{ Both balls white} ) = \frac{^{2}{}{C}_2}{^{9}{}{C}_2} = \frac{1}{36}\]
\[\text{ It can be shown in tabular form as follows . } \]
X 0 1 2
\[P(X) \ \ \frac {21}{36} \frac{14}{36} \frac{1}{36}\]
APPEARS IN
संबंधित प्रश्न
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?
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?
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 fair coin is tossed 8 times. Find the probability that it shows heads exactly 5 times.
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
Find the probability distribution of the number of sixes in three tosses of a die.
Three cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the mean and variance of number of red cards.
A coin is tossed 5 times. If X is the number of heads observed, find the probability distribution of X.
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?
Six coins are tossed simultaneously. Find the probability of getting
(i) 3 heads
(ii) no heads
(iii) at least one head
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 .
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.
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90% ?
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?
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
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.
Find the expected number of boys in a family with 8 children, assuming the sex distribution to be equally probable.
If the sum of the mean and variance of a binomial distribution for 6 trials is \[\frac{10}{3},\] find the distribution.
If in a binomial distribution mean is 5 and variance is 4, write the number of trials.
If in a binomial distribution n = 4, P (X = 0) = \[\frac{16}{81}\], then P (X = 4) equals
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
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 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 = 100 and p = 1/3, then P (X = r) is maximum when r =
In a binomial distribution, the probability of getting success is 1/4 and standard deviation is 3. Then, its mean is
Mark the correct alternative in the following question:
The probability of guessing correctly at least 8 out of 10 answers of a true false type examination 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
One of the condition of Bernoulli trials is that the trials are independent of each other.
Which one is not a requirement of a binomial distribution?
Suppose a random variable X follows the binomial distribution with parameters n and p, where 0 < p < 1. If P(x = r)/P(x = n – r) is independent of n and r, then p equals ______.
The sum of n terms of the series `1 + 2(1 + 1/n) + 3(1 + 1/n)^2 + ...` is
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.
A student is given a quiz with 10 true or false questions and he answers by sheer guessing. If X is the number of questions answered correctly write the p.m.f. of X. If the student passes the quiz by getting 7 or more correct answers what is the probability that the student passes the quiz?
