Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-2>Q 47

HARD

JEE Main/Advance

IMPORTANT

Earn 100

Mean and variance of a Binomial variate of $10$ trials of the experiment are in the ratio of $3 : 2$

50% studentsanswered this correctly

Important Questions on Probability

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-2>Q 48

A student appears for tests

I, II & III

. The student is successful if he passes either in tests

I & II

or tests

I & III

. The probabilities of the student passing in the tests

I, II & III

are

p, q & \frac{1}{2}

, respectively. If the probability that the student is successful is

\frac{1}{2},

then

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-2>Q 49

A student has to match three historical events i.e. Dandi March, Quit India Movement and Mahatma Gandhi's assassination with the years

1948, 1930

and

1942

and each event happens in different years. The student has no knowledge of the correct answers and decides to match the events and years randomly. Let

E_{1} : (0 \leq i \leq 3)

denote the event that the student gets exactly

i

correct answer, then

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-2>Q 50

For any two events

A & B

defined on a sample space,

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-2>Q 51

An unbiased coin is tossed

n

times. Let

X

denote the number of times head occurs. If

P (X = 4), P (X = 5)

and

P (X = 6)

are in

AP,

then the value of

n

can be

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-2>Q 52

A random variable

x

takes values

0, 1, 2, 3, \dots \dots,

with probability proportional to

(x + 1) {(\frac{1}{5})}^{x}

, then

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-2>Q 53

A square matrix of order

3 \times 3

is formed using the elements of the set

\{- 2016, 0, 2016\}

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-2>Q 58

A variable takes the values of

0, 1, 2, \dots \dots, n

with frequencies proportional to the binomial coefficients

{}^{n}C_{0}, {}^{n}C_{1}, {}^{n}C_{2}, \dots, {}^{n}C_{n},

then the mean of the distribution is

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-3>Q 2

Let

ω

be a complex cube root of unity with

ω \neq 1

. A fair die is thrown three times. If

r_{1}, r_{2}

and

r_{3}

are the numbers obtained on the die, then the probability that

ω^{r_{1}} + ω^{r_{2}} + ω^{r_{3}} = 0

is