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A fair octahedral die numbered $1, 2, . . . . ., 8$ is thrown seven times. Let $Q$ denote the number of prime numbers thrown. Find the probability that at least three prime numbers are thrown.

(Write answer in simplest fraction form)

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

In a binomial distribution, mean is

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and variance is

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then probability of success

(p) = . . . .

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answers on a true-false type examination is

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Let

C_{1}

and

C_{2}

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

\frac{2}{3}

and

\frac{1}{3}

, 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>Algebra>Probability>Bernoulli Trials and Binomial Distribution

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

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successes in the six trials of this experiment is

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The probability of a man hitting a target is

\frac{1}{10} .

The least number of shots required, so that the probability of his hitting the target at least once is greater than

\frac{1}{4},

is....

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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}

. If the probability that at most two machines will be out of service on the same day is

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

then

k

is equal to

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Mathematics>Algebra>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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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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For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is

\frac{4}{5},

then the probability that he is unable to solve less than two problems is

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A die is thrown

7

times. What is the probability that an even number turns up at least

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A shooter can hit a given target with probability

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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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99 %

chance of completely destroying the target, is

. . . . .

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The sum of mean and variance of a Binomial distribution

(\vec{B D})

for

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2.7

, then the binomial distribution

\vec{B D}

is given by

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2 n

unbiased coins are tossed. The probability of having the number of heads is not equal to the number of tails is

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20

and

4

, respectively, then the number of trials is ________

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Let a random variable

X

has a binomial distribution with mean

8

and variance 4. If

P (X \leq 2) = \frac{k}{2^{16}},

then the value of

k

is equal to

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Mathematics>Algebra>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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If the mean and the variance of a binomial variate

X

are

2 & 1

respectively, then the probability that

X

takes a value greater than or equal to one is:

A fair octahedral die numbered 1, 2, ....., 8 is thrown seven times. Let Q denote the number of prime numbers thrown. Find the probability that at least three prime numbers are thrown. (Write answer in simplest fraction form)

Important Questions on Probability

Learn and Prepare for any exam you want !

A fair octahedral die numbered $1, 2, . . . . ., 8$ is thrown seven times. Let $Q$ denote the number of prime numbers thrown. Find the probability that at least three prime numbers are thrown.

(Write answer in simplest fraction form)