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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 $Y$ ?

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Mathematics>Statistics and Probability>Probability>Bernoulli Trials and Binomial Distribution

Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is

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and variance is

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Let

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C_{2}

be two biased coins such that the probabilities of getting head in a single toss are

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and

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, respectively. Suppose

α

is the number of heads that appear when

C_{1}

is tossed twice, independently, and suppose

β

is the number of heads that appear when

C_{2}

is tossed twice, independently. Then the probability that the roots of the quadratic polynomial

x^{2} - α x + β

are real and equal, is

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Mathematics>Statistics and Probability>Probability>Bernoulli Trials and Binomial Distribution

An experiment succeeds twice as often as it fails. The probability of at least

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Mathematics>Statistics and Probability>Probability>Bernoulli Trials and Binomial Distribution

In a workshop, there are five machines and the probability of any one of them to be out of service on a day is

\frac{1}{4}

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{(\frac{3}{4})}^{3} k,

then

k

is equal to

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Mathematics>Statistics and Probability>Probability>Bernoulli Trials and Binomial Distribution

If on an average

9

mountain climbers out of

10

return safely, what is the probability that with

5

climbers out, at least

4

will return safely?

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Mathematics>Statistics and Probability>Probability>Bernoulli Trials and Binomial Distribution

The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least

90 %

is:

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Mathematics>Statistics and Probability>Probability>Bernoulli Trials and Binomial Distribution

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Mathematics>Statistics and Probability>Probability>Bernoulli Trials and Binomial Distribution

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A shooter can hit a given target with probability

\frac{1}{4} .

She keeps firing a bullet at the target until she hits it successfully three times, and then she stops firing. The probability that she fires exactly six bullets lies in the interval

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A coin is tossed

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\vec{B D}

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Mathematics>Statistics and Probability>Probability>Bernoulli Trials and Binomial Distribution

Let $X$ be the discrete random variable representing the number $(x)$ appeared on the face of a biased die when it is rolled. The probability distribution of $X$ is

$X = x$	$1$	$2$	$3$	$4$	$5$	$6$
$P (X = x)$	$0.1$	$0.15$	$0.3$	$0.25$	$k$	$k$

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Mathematics>Statistics and Probability>Probability>Bernoulli Trials and Binomial Distribution

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Mathematics>Statistics and Probability>Probability>Bernoulli Trials and Binomial Distribution

For the following distribution function $F (x)$ of a random variable $X$

$x$	$1$	$2$	$3$	$4$	$5$	$6$
$F (x)$	$0.2$	$0.37$	$0.48$	$0.62$	$0.85$	$1$

$P (3 < X \leq 5) =$

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Mathematics>Statistics and Probability>Probability>Bernoulli Trials and Binomial Distribution

If the mean and the variance of a binomial variate

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Let X and Y be two random variables such that X+Y=100. If X follows Binomial distribution with parameters n=100 and p=45, what is the variance of Y?

Important Questions on Probability

Learn and Prepare for any exam you want !

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 $Y$ ?