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Five cards are drawn successively, with replacement, from a well-shuffled deck of $52$ cards. The probability that only $3$ cards are spades is

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Important Questions on Probability

HARD

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

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

EASY

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

In a binomial distribution, mean is

18

and variance is

12

then probability of success

(p) = . . . .

MEDIUM

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

The probability of guessing correctly at least

8

out of

10

answers on a true-false type examination is

HARD

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

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

HARD

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

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

5

successes in the six trials of this experiment is

HARD

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

In a bombing attack, there is

50 %

chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least

99 %

chance of completely destroying the target, is

. . . . .

HARD

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

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

HARD

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

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?

HARD

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

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:

HARD

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

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

MEDIUM

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

A die is thrown

7

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

4

times?

MEDIUM

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

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

HARD

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

A coin is tossed

7

times. Each time a man calls head. The probability that he wins the toss at least four times is

MEDIUM

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

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....

MEDIUM

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

The sum of mean and variance of a Binomial distribution

(\vec{B D})

for

3

trials is

2.7

, then the binomial distribution

\vec{B D}

is given by

MEDIUM

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

2 n

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

MEDIUM

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

If the mean and standard deviation of a binomial distribution are

20

and

4

, respectively, then the number of trials is ________

MEDIUM

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

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

MEDIUM

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

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

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

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

HARD

Reasoning and General Awareness>Mathematics>Probability>Probability and its Applications

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:

Five cards are drawn successively, with replacement, from a well-shuffled deck of 52 cards. The probability that only 3 cards are spades is

Important Questions on Probability

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Five cards are drawn successively, with replacement, from a well-shuffled deck of $52$ cards. The probability that only $3$ cards are spades is