In a Binomial distribution, the mean is three times its variance. What is the probability of exactly 3 successes out of 5 trials?

If mean and variance of a Binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than 1 is

Let X and Y be two random variables such that X + Y = 100. If X follows Binomial distribution with parameters n = 100 and p = \(\frac{4}{5}\), what is the variance of Y?  

Let the random variables X follow B (6, p) If \(16{\rm{\;P\;}}\left( {{\rm{X}} = 4} \right) = {\rm{P\;}}\left( {{\rm{X}} = 2} \right)\) , then what is the value of p

Consider a random variable X which follows Binomial distribution with parameters n = 10 and \(\rm p = \dfrac{1}{5}\) . Then Y = 10 - X follows Binomial distribution with parameters n' and p' respectively given by

In a binomial distribution, the mean is \(\dfrac{2}{3}\) and variance is \(\dfrac{5}{9}\) . What is the probability that random variable D = 2?

If a fair die is rolled 4 times, then what is the probability that there are exactly 2 sixes?

What is the probability that no one out of 6 workers suffers from a disease?

8 coins are tossed simultaneously. The probability of getting at least 6 heads is

In a Binomial distribution, the mean is three times its variance. What is the probability of exactly 3 successes out of 5 trials?

If mean and variance of a Binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than 1 is

For Binomial distribution, n = 10 and p = 0.6, E(X ²) (second moment about origin) is:

Indicate the correct answer for the combination from the following regarding the conditions for the applicability of a binominal distribution:

(a) There are n independent trials

(b) Each trial has only two possible outcomes

(c) The probabilities of two outcomes do not remain constant

(d) The trials are independent

Which of the following options is correct?