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$F i v e$ horses are in a race. $M r . A$ selects two of the horses at random and bets on them. The probability that $M r . A$ selected the winning horse is

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Important Questions on Probability

MEDIUM

Mathematics>Statistics and Probability>Probability>Total Probability and Bayes' Theorem

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:

EASY

Mathematics>Statistics and Probability>Probability>Total Probability and Bayes' Theorem

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>Total Probability and Bayes' Theorem

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>Total Probability and Bayes' Theorem

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?

HARD

Mathematics>Statistics and Probability>Probability>Total Probability and Bayes' Theorem

A

and

B

are two independent witnesses (i.e., there is no collision between them) in a case. The probability that

A

will speak the truth is

x

and the probability that

B

will speak the truth is

y .

A

and

B

agree in a certain statement. The probability that the statement is true is

MEDIUM

Mathematics>Statistics and Probability>Probability>Total Probability and Bayes' Theorem

The probability of guessing correctly at least

8

out of

10

answers on a true-false type examination is

EASY

Mathematics>Statistics and Probability>Probability>Total Probability and Bayes' Theorem

A

and

B

are two events such that

P (A) \neq 0

and

P (B| A) = 1

, then

EASY

Mathematics>Statistics and Probability>Probability>Total Probability and Bayes' Theorem

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>Total Probability and Bayes' Theorem

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:

EASY

Mathematics>Statistics and Probability>Probability>Total Probability and Bayes' Theorem

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>Total Probability and Bayes' Theorem

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>Total Probability and Bayes' Theorem

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:

MEDIUM

Mathematics>Statistics and Probability>Probability>Total Probability and Bayes' Theorem

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>Total Probability and Bayes' Theorem

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>Total Probability and Bayes' Theorem

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>Total Probability and Bayes' Theorem

A die is thrown

7

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

4

times?

EASY

Mathematics>Statistics and Probability>Probability>Total Probability and Bayes' Theorem

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

MEDIUM

Mathematics>Statistics and Probability>Probability>Total Probability and Bayes' Theorem

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

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

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

MEDIUM

Mathematics>Statistics and Probability>Probability>Total Probability and Bayes' Theorem

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

HARD

Mathematics>Statistics and Probability>Probability>Total Probability and Bayes' Theorem

A car manufacturing factory has two plants

X

and

Y .

Plant

X

manufactures

70 %

of cars and plant

Y

manufactures

30 %

of cars.

80 %

of cars at plant

X

and

90 %

of cars at plant

Y

are rated as standard quality. A car is chosen at random and is found to be standard quality. The probability that it has come from plant

X

Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is

Important Questions on Probability

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$F i v e$ horses are in a race. $M r . A$ selects two of the horses at random and bets on them. The probability that $M r . A$ selected the winning horse is