Binomial distribution Test 1

For a binomial distribution with $n = 6$, if $9P(X = 4) = P(X = 2)$, what is the value of $q$?

A man takes 11 steps, moving forward with probability 0.4 and backward with probability 0.6. What is the probability that he ends up one step away from the starting point?

The sum of the mean and variance of a binomial distribution for 10 trials is $\frac{15}{2}$. What is the variance?

The number of successes in an experiment is twice the number of failures. What is the probability that there will be at least 4 successes in the next 6 trials?

An irregular six-faced die is thrown. The probability of getting 3 even numbers in 5 throws is twice the probability of getting 2 even numbers. In 6804 sets of 5 throws, how many times would you expect to get no even number?

Let X be a random variable having a binomial distribution $B(7, p)$. If $P(X = 3) = 5P(X = 4)$, then what is the variance of X?

The sum of the mean and variance of a binomial distribution for 5 trials is 1.8. What is the value of $p$?

For an initial screening, a candidate is given 50 problems. The probability a candidate can solve a problem is $\frac{4}{5}$. What is the probability the candidate is unable to solve less than two problems?

A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random and sent to a retail store. What is the probability that the store will receive at most one defective bulb?

Let $X \sim B(6, \frac{1}{2})$. What is $P[|x-4| < 2]$?

Let a random variable X have a binomial distribution with mean 8 and variance 4. If $P(x \leq 2) = \frac{k}{2^{16}}$, then what is the value of k?

A multiple choice examination has 5 questions, each with 3 options, only 1 of which is correct. What is the probability that a student gets 4 or more correct answers just by guessing?

In a binomial distribution of 5 independent trials, the probabilities of exactly 1 and 2 successes are 0.4096 and 0.2048 respectively. What is the probability of getting exactly 4 successes?

Let X be a random variable having Binomial distribution B(7, p). If P[X = 3] = 5P[X = 4], then variance of X is

If the sum of the mean and the variance of a Binomial distribution for 5 trials is 1.8, then the value of p is

Given a binomial distribution where $n = 10$ and $p = 0.4$, what is the value of $E(X^2)$?

In an experiment, the probability of success is $\frac{3}{4}$ times the probability of failure. What is the probability of at least one success in 5 trials?

In a binomial distribution, the mean is 18, and the variance is 12. What is the value of $p$?

A person buys 5 lottery tickets. The probability of winning a prize on a single ticket is $\frac{1}{4}$. What is the probability that the person wins at least one prize?

A box contains 8 batteries, 3 of which are defective. A person randomly selects two batteries. If X is the number of defective batteries selected, what is $P(X \leq 1)$?

The probability that a person survives a certain operation is 0.2. If 5 patients undergo similar operations, what is the probability that exactly four will survive?

A bomb has a probability of 0.2 of missing its target. If 10 bombs are dropped, what is the probability that exactly 2 will hit the target?

A basketball player makes a basket with a probability of 0.4. What is the probability that the player makes exactly three baskets in four attempts?

A die is thrown 100 times. What is the standard deviation of getting an even number?

It is observed that 25% of child labor cases reported to the police are solved. If 6 new cases are reported, what is the probability that at least 5 of them will be solved?

If $X \sim B(4, p)$ and $P(X = 0) = \frac{16}{81}$, then what is $P(X = 4)$?

In an entrance test, 30% of students are science students. If 5 students are randomly selected, what is the probability that 2 of them are science students?

For a binomial variable $X$, the mean is 2 and the variance is 1. What are the odds in favor of $X = 0$?

The incidence of a certain occupational disease in an industry is such that workmen have a 10% chance of suffering from it. Out of 5 workmen, what is the probability that 3 or more will contract the disease?

A man hits a target with a probability of $\frac{3}{4}$. If he tries 5 times, what is the probability that he will hit the target exactly 3 times?

Three dice are thrown together. What is the probability of getting a sum of 5?

Eight coins are tossed simultaneously. What is the probability of getting exactly 6 heads?

An experiment succeeds twice as often as it fails. In 4 trials, what is the probability that there will be at most 3 successes?

A bag contains 2 white and 4 black balls. A ball is drawn 5 times with replacement. What is the probability that at least 3 of the balls drawn are white?