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.

EASY

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The number of $(a, b, c),$ where $a, b, c$ are positive integers such that $abc = 30$ , is

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Important Questions on Probability

MEDIUM

Mathematics>Algebra>Probability>Basics of 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})

HARD

Mathematics>Algebra>Probability>Basics of Probability

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

EASY

Mathematics>Algebra>Probability>Basics of 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)

MEDIUM

Mathematics>Algebra>Probability>Basics of Probability

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

Mathematics>Algebra>Probability>Basics of Probability

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

Mathematics>Algebra>Probability>Basics of Probability

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

Mathematics>Algebra>Probability>Basics of Probability

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

MEDIUM

Mathematics>Algebra>Probability>Basics of Probability

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:

MEDIUM

Mathematics>Algebra>Probability>Basics of Probability

The probability of guessing correctly at least

8

out of

10

answers on a true-false type examination is

MEDIUM

Mathematics>Algebra>Probability>Basics of 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>Algebra>Probability>Basics of Probability

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

EASY

Mathematics>Algebra>Probability>Basics of 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>Algebra>Probability>Basics of Probability

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

EASY

Mathematics>Algebra>Probability>Basics of Probability

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

MEDIUM

Mathematics>Algebra>Probability>Basics of Probability

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 :

MEDIUM

Mathematics>Algebra>Probability>Basics of Probability

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

EASY

Mathematics>Algebra>Probability>Basics of Probability

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

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

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

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

EASY

Mathematics>Algebra>Probability>Basics of 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:

EASY

Mathematics>Algebra>Probability>Basics of Probability

A

and

B

are two events such that

P (A) \neq 0

and

P (B| A) = 1

, then

MEDIUM

Mathematics>Algebra>Probability>Basics of Probability

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

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

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

The number of a,b,c, where a,b,c are positive integers such that abc=30, is

Important Questions on Probability

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The number of $(a, b, c),$ where $a, b, c$ are positive integers such that $abc = 30$ , is