Advertisements
Advertisements
Question
A bag contains 1 red and 3 white balls. Find the probability distribution of the number of red balls if 2 balls are drawn at random from the bag one-by-one without replacement.
Solution
Let X be the random variable defined as the number of red balls.
Then X = 0, 1
P(X = 0) = `3/4 xx 2/3 = 6/12 = 1/2`
P(X = 1) = `1/4 xx 3/3 + 3/4 xx 1/3 = 6/12 = 1/2`
Probability Distribution Table:
| X | 0 | 1 |
| P(X) | `1/2` | `1/2` |
APPEARS IN
RELATED QUESTIONS
State the following are not the probability distributions of a random variable. Give reasons for your answer.
| Y | -1 | 0 | 1 |
| P(Y) | 0.6 | 0.1 | 0.2 |
Suppose that two cards are drawn at random from a deck of cards. Let X be the number of aces obtained. Then the value of E(X) is
(A) `37/221`
(B) 5/13
(C) 1/13
(D) 2/13
Three persons A, B and C shoot to hit a target. If A hits the target four times in five trials, B hits it three times in four trials and C hits it two times in three trials, find the probability that:
1) Exactly two persons hit the target.
2) At least two persons hit the target.
3) None hit the target.
The probability distribution function of a random variable X is given by
| xi : | 0 | 1 | 2 |
| pi : | 3c3 | 4c − 10c2 | 5c-1 |
where c > 0 Find: P (1 < X ≤ 2)
Find the probability distribution of the number of heads, when three coins are tossed.
Five defective bolts are accidently mixed with twenty good ones. If four bolts are drawn at random from this lot, find the probability distribution of the number of defective bolts.
Find the mean and standard deviation of each of the following probability distribution :
| xi : | -5 | -4 | 1 | 2 |
| pi : | \[\frac{1}{4}\] | \[\frac{1}{8}\] | \[\frac{1}{2}\] | \[\frac{1}{8}\] |
Two bad eggs are accidently mixed up with ten good ones. Three eggs are drawn at random with replacement from this lot. Compute the mean for the number of bad eggs drawn.
A fair die is tossed. Let X denote 1 or 3 according as an odd or an even number appears. Find the probability distribution, mean and variance of X.
A fair coin is tossed four times. Let X denote the longest string of heads occurring. Find the probability distribution, mean and variance of X.
If a random variable X has the following probability distribution:
| X : | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| P (X) : | a | 3a | 5a | 7a | 9a | 11a | 13a | 15a | 17a |
then the value of a is
Find the probability distribution of the number of doublets in three throws of a pair of dice and find its mean.
Five bad oranges are accidently mixed with 20 good ones. If four oranges are drawn one by one successively with replacement, then find the probability distribution of number of bad oranges drawn. Hence find the mean and variance of the distribution.
For the following probability density function (p. d. f) of X, find P(X < 1) and P(|x| < 1)
`f(x) = x^2/18, -3 < x < 3`
= 0, otherwise
A fair coin is tossed 12 times. Find the probability of getting at least 2 heads .
If random variable X has probability distribution function.
f(x) = `c/x`, 1 < x < 3, c > 0, find c, E(x) and Var(X)
The expenditure Ec of a person with income I is given by Ec = (0.000035) I2 + (0. 045) I. Find marginal propensity to consume (MPC) and average propensity to consume (APC) when I = 5000.
If X ∼ N (4,25), then find P(x ≤ 4)
Alex spends 20% of his income on food items and 12% on conveyance. If for the month of June 2010, he spent ₹900 on conveyance, find his expenditure on food items during the same month.
The p.m.f. of a random variable X is
`"P"(x) = 1/5` , for x = I, 2, 3, 4, 5
= 0 , otherwise.
Find E(X).
A card is drawn at random and replaced four times from a well shuftled pack of 52 cards. Find the probability that -
(a) Two diamond cards are drawn.
(b) At least one diamond card is drawn.
An urn contains 5 red and 2 black balls. Two balls are drawn at random. X denotes number of black balls drawn. What are possible values of X?
Find expected value and variance of X, where X is number obtained on uppermost face when a fair die is thrown.
A sample of 4 bulbs is drawn at random with replacement from a lot of 30 bulbs which includes 6 defective bulbs. Find the probability distribution of the number of defective bulbs.
The probability that a bulb produced by a factory will fuse after 200 days of use is 0.2. Let X denote the number of bulbs (out of 5) that fuse after 200 days of use. Find the probability of X = 0
Solve the following problem :
Following is the probability distribution of a r.v.X.
| x | – 3 | – 2 | –1 | 0 | 1 | 2 | 3 |
| P(X = x) | 0.05 | 0.1 | 0.15 | 0.20 | 0.25 | 0.15 | 0.1 |
Find the probability that X is even.
Let X be a discrete random variable. The probability distribution of X is given below:
| X | 30 | 10 | – 10 |
| P(X) | `1/5` | `3/10` | `1/2` |
Then E(X) is equal to ______.
Let X be a discrete random variable whose probability distribution is defined as follows:
P(X = x) = `{{:("k"(x + 1), "for" x = 1"," 2"," 3"," 4),(2"k"x, "for" x = 5"," 6"," 7),(0, "Otherwise"):}`
where k is a constant. Calculate E(X)
A box contains 30 fruits, out of which 10 are rotten. Two fruits are selected at random one by one without replacement from the box. Find the probability distribution of the number of unspoiled fruits. Also find the mean of the probability distribution.
