Advertisements
Advertisements
प्रश्न
A fair coin is tossed 8 times. Find the probability that it shows heads at least once
Advertisements
उत्तर
Let X = Number of heads
p = probability of getting head in one toss
p = `1/2`
q = `1 - p = 1 - 1/2 = 1/2`
Given n = 8
`x ~ B(8, 1/2)`
The p.m.f. of X is given as
P(X = x) = `""^nC_xp^xq^(n - x)`
i.e P(x) = `""^8C_x(1/2)^x(1/2)^(8 - x), x = 0, 1, 2, 3,......,8`
P (getting heads at least once)
P[X > = 1] = 1 – P[X = 0]
= 1 – P(0)
= `1-""^8C_0(1/2)^0(1/2)^(8-0)`
= `1 - (1/2)^8`
= `1 - 1/256`
= `255/256`
P[X > = 1] = 0.996
APPEARS IN
संबंधित प्रश्न
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?
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?
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
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?
An experiment succeeds twice as often as it fails. Find the probability that in the next 6 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 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.
Can the mean of a binomial distribution be less than its variance?
If a random variable X follows a binomial distribution with mean 3 and variance 3/2, find P (X ≤ 5).
In a binomial distribution, if n = 20 and q = 0.75, then write its mean.
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 of a binomial distribution is 20 and its standard deviation is 4, find p.
If the mean and variance of a random variable X with a binomial distribution are 4 and 2 respectively, find P (X = 1).
If in a binomial distribution n = 4 and P (X = 0) = \[\frac{16}{81}\] , find q.
If the mean and variance of a binomial distribution are 4 and 3, respectively, find the probability of no success.
If for a binomial distribution P (X = 1) = P (X = 2) = α, write P (X = 4) in terms of α.
An unbiased coin is tossed 4 times. Find the mean and variance of the number of heads obtained.
If in a binomial distribution n = 4, P (X = 0) = \[\frac{16}{81}\], then P (X = 4) equals
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
If X follows a binomial distribution with parameters n = 100 and p = 1/3, then P (X = r) is maximum when r =
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
Mark the correct alternative in the following question:
Which one is not a requirement of a binomial dstribution?
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
For X ~ B(n, p) and P(X = x) = `""^8"C"_x(1/2)^x (1/2)^(8 - x)`, then state value of n and p
If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9, P(X = 3), then p = ______.
The sum of n terms of the series `1 + 2(1 + 1/n) + 3(1 + 1/n)^2 + ...` is
If x4 occurs in the tth term in the expansion of `(x^4 + 1/x^3)^15`, then the value oft is equal to:
If the coefficients of x7 and x8 in `(2 + x/3)^n` are equal, then n is
In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is:-
If a fair coin is tossed 10 times. Find the probability of getting at most six heads.
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 the sum of mean and variance of a binomial distribution is `25/9` for 5 trials, find p.
If X ∼ B(n, p), n = 6 and 9 P(X = 4) = P(X = 2), then find the value of p.
For the binomial distribution X ∼ B(n, p), n = 6 and P(X = 4) = P(X = 2). find p.
