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In a certain population $10 %$ of the people are rich, $5 %$ are famous and $3 %$ are rich and famous. The probability that a person picked at random from the population is either famous or rich but not both, is equal to

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Important Questions on Probability

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Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

Six persons $A, B, C, X, Y & Z$ go for an interview. What is the probability of selection of $A$ and $Y$ in the interview?

MEDIUM

Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

Assume that each born child is equally likely to be a boy or girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is:

MEDIUM

Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

The probability of guessing correctly at least

8

out of

10

answers on a true-false type examination is

MEDIUM

Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

Two letters are chosen from the letters of the word 'EQUATIONS'. The probability that one is vowel and the other is consonant is

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Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

A

and

B

are any two events such that

P (A) + P (B) - P (A a n d B) = P (A)

, then

MEDIUM

Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set $S = {1, 2, 3, 4, 5, 6, 7}$ and reports that it is even. The probability that it is actually even is

EASY

Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

Let

A

and

B

be two events such that the probability that exactly one of them occurs is

\frac{2}{5}

and the probability that

A

B

occurs is

\frac{1}{2}

, then the probability of both of them occur together is

MEDIUM

Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

Three numbers are chosen at random without replacement from

{1, 2, 3, \dots \dots, 8}

. The probability that their minimum is

3

, given that their maximum is

6

, is

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Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

A

and

B

are two events such that

P (A) \neq 0

and

P (B| A) = 1

, then

MEDIUM

Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

A bag contains

4

red and

6

black balls. A ball is drawn at random from the bag, its color is observed and this ball along with two additional balls of the same color are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is:

EASY

Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

It is given that the events

A

and

B

are such that

P (A) = \frac{1}{4}, P (A ∣ B) = \frac{1}{2}

and

P (B ∣ A) = \frac{2}{3}

. Then

P (B)

EASY

Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

A

and

B

are events with

P (A \cup B) = \frac{3}{4}, P (A^{'}) = \frac{2}{3}

and

P (A \cap B) = \frac{1}{4}

then

P (B)

EASY

Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

Let

A

and

B

are two independent events. If the probability that both

A

and

B

occur together is

\frac{1}{6}

and the probability that neither of them occurs is

\frac{1}{3}

, then the probability of occurrence of

A

EASY

Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

In a college, $\frac{1}{5} t h$ of the girls and $\frac{1}{8} th$ of the boys took part in a social camp. The total number of students in the college took part in the camp is:

MEDIUM

Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

A die is thrown

7

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

4

times?

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Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

Two numbers are selected at random from the set

\{1, 2, 3, \dots \dots, 13\} .

If the sum of the selected numbers is even, the probability that both the numbers are odd is

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Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

The probability that atleast one of the events

A

and

B

occur is

0.6 .

A

and

B

occur simultaneously with probability

0.2

, then

P (\bar{A}) + P (\bar{B})

MEDIUM

Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

Let

A

and

B

be two non-null events such that

A \subset B .

Then, which of the following statements is always correct?

MEDIUM

Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

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

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

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

EASY

Mathematics>Statistics and Probability>Probability>Axiomatic Approach to Probability

An urn contains

5

red and

2

green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is:

In a certain population 10% of the people are rich, 5% are famous and 3% are rich and famous. The probability that a person picked at random from the population is either famous or rich but not both, is equal to

Important Questions on Probability

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In a certain population $10 %$ of the people are rich, $5 %$ are famous and $3 %$ are rich and famous. The probability that a person picked at random from the population is either famous or rich but not both, is equal to