Advertisements
Advertisements
प्रश्न
A coin is tossed 5 times. If X is the number of heads observed, find the probability distribution of X.
उत्तर
Let X = number of heads in 5 tosses. Then the binomial distribution for X has n =5,
\[ = \frac{^{5}{}{C}_r}{2^5}\]
\[\text{ Substituting r = 0, 1, 2, 3, 4, 5 we get the following probability disrtribution } . \]
X 0 1 2 3 4 5
\[P(X) \frac{1}{32} \frac{5}{32} \frac{10}{32} \frac{10}{32} \frac{5}{32} \frac{1}{32}\]
APPEARS IN
संबंधित प्रश्न
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.
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?
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)
A couple has two children, Find the probability that both children are females, if it is known that the elder child is a female.
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?
Find the probability distribution of the number of sixes in three tosses of a die.
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 die is thrown 5 times. Find the probability that an odd number will come up exactly three times.
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 none of the bulbs is 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 exactly two bulbs are defective
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.
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.
The mean and variance of a binomial distribution are \[\frac{4}{3}\] and \[\frac{8}{9}\] respectively. Find P (X ≥ 1).
In a group of 200 items, if the probability of getting a defective item is 0.2, write the mean of the distribution.
If the mean and variance of a random variable X with a binomial distribution are 4 and 2 respectively, find P (X = 1).
If for a binomial distribution P (X = 1) = P (X = 2) = α, write P (X = 4) in terms of α.
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?
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
If X is a binomial variate with parameters n and p, where 0 < p < 1 such that \[\frac{P\left( X = r \right)}{P\left( X = n - r \right)}\text{ is } \] independent of n and r, then p equals
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
A coin is tossed 10 times. The probability of getting exactly six heads is
In a binomial distribution, the probability of getting success is 1/4 and standard deviation is 3. Then, its mean 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
Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that none is a spade ?
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
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
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
An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is ______.
In three throws with a pair of dice find the chance of throwing doublets at least twice.
