Advertisements
Advertisements
प्रश्न
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
पर्याय
49, 50
50, 51
51, 52
None of these
उत्तर
49, 50
When a coin is tossed 99 times, the number of heads X follows a binomial distribution with
\[p = q = \frac{1}{2} = 0 . 5\]
\[P(X = r) = ^{n}{}{C}_r (0 . 5 )^r (0 . 5 )^{n - r} = ^{n}{}{C}_r (0 . 5 )^n \]
\[As (0 . 5 )^n \text{ is common to all r it is enough if we find the maximum of }\ ^{\ n}{}{C}_r . \]
\[\text{ We know that for odd number of n, there will be two equal maximum terms, } \]
\[\text{ i . e . when } r = \frac{n - 1}{2}\text{ and } r = \frac{n + 1}{2}\]
\[\text{ Hence,} \ n = 99 \]
\[\text{ So, the maximum is obtained when r = 49 or } 50\]
APPEARS IN
संबंधित 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.
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?
It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?
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.
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?
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.
The probability of a man hitting a target is 1/4. If he fires 7 times, what is the probability of his hitting the target at least twice?
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?
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 box contains 100 tickets, each bearing one of the numbers from 1 to 100. If 5 tickets are drawn successively with replacement from the box, find the probability that all the tickets bear numbers divisible by 10.
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?
A coin is tossed 5 times. If X is the number of heads observed, find the probability distribution of X.
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 .
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 .
Suppose X has a binomial distribution with n = 6 and \[p = \frac{1}{2} .\] Show that X = 3 is the most likely outcome.
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?
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
Determine the binomial distribution whose mean is 20 and variance 16.
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.
Find the expected number of boys in a family with 8 children, assuming the sex distribution to be equally probable.
If a random variable X follows a binomial distribution with mean 3 and variance 3/2, find P (X ≤ 5).
If the sum of the mean and variance of a binomial distribution for 6 trials is \[\frac{10}{3},\] find the distribution.
If the mean and variance of a binomial variate X are 2 and 1 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 in a binomial distribution n = 4, P (X = 0) = \[\frac{16}{81}\], then P (X = 4) equals
A fair coin is tossed 100 times. The probability of getting tails an odd number of times is
Let X denote the number of times heads occur in n tosses of a fair coin. If P (X = 4), P (X= 5) and P (X = 6) are in AP, the value of n 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 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
If the mean and variance of a binomial distribution are 4 and 3, respectively, the probability of getting exactly six successes in this distribution is
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
One of the condition of Bernoulli trials is that the trials are independent of each other.
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 ______.
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.
