Let A and B be two events such that P A ∪ B = 1 6 , P A ∩ B = 1 4 , and P A = 1 4 , where A ¯ stands for complement of event A . Then events A and B are

independent but not equally likely.

mutually exclusive and independent.

equally likely but not independent.

equally likely and mutually exclusive.

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In a dice game, one fair is used. The player wins if he rolls either $1$ or $6$ . He losses if he turns up any other face. What is the expected winning for one roll of the die?

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Important Questions on Venn Diagrams

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General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

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})

HARD

General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

Let

A

and

B

be two events such that

P (A \cup B) = \frac{1}{6}, P (A \cap B) = \frac{1}{4}

, and

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

, where

\bar{A}

stands for complement of event

A

. Then events

A

and

B

are

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General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

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)

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General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

A six faced die is so biased that it is thrice likely to show an even number than an odd number, when thrown. If the die is thrown twice, the probability that sum of the numbers on the die is even, is

HARD

General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

Let two fair six-faced dice

A

and

B

be thrown simultaneously. If

E_{1}

is the event that die

A

shows up four,

E_{2}

is the event that die

B

shows up two and

E_{3}

is the event that the sum of numbers on both dice is odd, then which of the following statements is not true?

HARD

General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

Four dice are thrown simultaneously and the numbers shown on these dice are recorded in

2 \times 2

matrices. The probability that such formed matrices have all different entries and are non-singular, is:

HARD

General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

A bag contains

6

red balls and

10

green balls.

3

balls are drawn from it one by one randomly without replacement. If the

3^{rd}

drawn ball is red, then the probability that the first two drawn balls are green is

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General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

Each of the persons

A

and

B

independently tosses three fair coins. The probability that both of them get the same number of heads is:

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General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

The probability of guessing correctly at least

8

out of

10

answers on a true-false type examination is

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General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

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?

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General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

A

and

B

try to hit a target. The probability that

A

hits the target is

\frac{7}{10}

and the probability that

B

hits the target is

\frac{4}{10} .

If these two events are independent, the probability that

B

hits the target, given that the target is hit, is

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A

and

B

are two events such that

P (A) \neq 0

and

P (B| A) = 1

, then

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General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

When a certain biased die is rolled, a particular face occurs with probability $\frac{1}{6} - x$ and its opposite face occurs with probability $\frac{1}{6} + x .$ All other faces occur with probability $\frac{1}{6} .$

Note that opposite faces sum to $7$ in any die. If $0 < x < \frac{1}{6},$ and the probability of obtaining total sum $= 7,$ when such a die is rolled twice, is $\frac{13}{96},$ then the value of $x$ is

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General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

It is given that 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)

is equal to

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General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

A fair die is tossed until six is obtained on it. Let

X

be the number of required tosses, then the conditional probability

P (X ⩾ 5 ∣ X > 2)

is :

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General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

A signal which can be green or red with probability

\frac{4}{5}

and

\frac{1}{5}

respectively, is received by station

A

and then transmitted to station

B

. The probability of each station receiving the signal correctly is

\frac{3}{4}

. If the signal received at station

B

is green, then the probability that the original signal is green, is

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General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

If $A$ and $B$ are events such that $P (A) = 0.42, P (B) = 0.48$ and $P (A and B) = 0 .16$ . Then,

$I .$ $P (not A) =0 . 58$

$II .$ $P (not B) = 0.52$

$III .$ $P (A or B) = 0.47$

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General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

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:

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General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

A

and

B

are any two events such that

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

, then

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General Intelligence and Reasoning>Numerical Reasoning>Venn Diagrams>Logical Venn Diagrams

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

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

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

In a dice game, one fair is used. The player wins if he rolls either 1 or 6. He losses if he turns up any other face. What is the expected winning for one roll of the die?

Important Questions on Venn Diagrams

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In a dice game, one fair is used. The player wins if he rolls either $1$ or $6$ . He losses if he turns up any other face. What is the expected winning for one roll of the die?