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

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A random variable $x$ takes values $0, 1, 2, 3, \dots \dots,$ with probability proportional to $(x + 1) {(\frac{1}{5})}^{x}$ , then

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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\}

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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

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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

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

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 was green is

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Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-3>Q 5

Let

E

and

F

be two independent events. The probability that exactly one of them occurs is

\frac{11}{25}

and the probability of none of them occurring is

\frac{2}{25} .

If

P (T)

denotes the probability of occurrence of the event

T,

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-3>Q 6

A ship is fitted with three engines

E_{1}, E_{2}

and

E_{3} .

The engines function independently of each other with respective probabilities

\frac{1}{2}, \frac{1}{4}

and

\frac{1}{4} .

For the ship to be operational at least two of its engines must function. Let

X

denote the event that the ship is operational and let

X_{1}, X_{2}

and

X_{3}

denotes, respectively, the events that the engines

E_{1} E_{2}

and

E_{3}

are functioning. Which of the following is (are) true?

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Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-3>Q 7

Four fair dice $D_{1}, D_{2}, D_{3}$ and $D_{4}$ each having six faces numbered $1, 2, 3, 4, 5$ and $6$ are rolled simultaneously. The probability that $D_{4}$ shows a number appearing on one of $D_{1}, D_{2}$ and $D_{3}$ is

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Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-3>Q 8

Let

X

and

Y

be two events such that

P (X ∣ Y) = \frac{1}{2}, P (Y ∣ X) = \frac{1}{3}

and

P (X \cap Y) = \frac{1}{6} .

Which of the following (are) correct?