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2 votes
1 answer
1
Two identical cube shaped dice each with faces numbered $1$ to $6$ are rolled simultaneously. The probability that an even number is rolled out on each dice is: $\frac{1}{36}$ $\frac{1}{12}$ $\frac{1}{8}$ $\frac{1}{4}$
asked Mar 1 in Quantitative Aptitude jothee 194 views
1 vote
1 answer
2
A box contains $15$ blue balls and $45$ black balls. If $2$ balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball, is _____ $\frac{3}{16}$ $\frac{45}{236}$ $\frac{1}{4}$ $\frac{3}{4}$
asked Mar 1 in Quantitative Aptitude jothee 296 views
1 vote
1 answer
3
Let $X$ be a continuous random variable denoting the temperature measured. The range of temperature is $[0, 100]$ degree Celsius and let the probability density function of $X$ be $f\left ( x \right )=0.01$ for $0\leq X\leq 100$. The mean of $X$ is __________ $2.5$ $5.0$ $25.0$ $50.0$
asked Feb 20 in Quantitative Aptitude Arjun 180 views
4 votes
1 answer
4
For a given biased coin, the probability that the outcome of a toss is a head is $0.4$. This coin is tossed $1,000$ times. Let $X$ denote the random variable whose value is the number of times that head appeared in these $1,000$ tosses. The standard deviation of $X$ (rounded to $2$ decimal place) is _________
asked Feb 18 in Probability Arjun 836 views
5 votes
3 answers
5
In an examination, a student can choose the order in which two questions ($\textsf{QuesA}$ and $\textsf{QuesB}$) must be attempted. If the first question is answered wrong, the student gets zero marks. If the first question is answered correctly and the second question is not ... and then $\textsf{QuesA}$. Expected marks $22$. First $\textsf{QuesA}$ and then $\textsf{QuesB}$. Expected marks $16$.
asked Feb 18 in Probability Arjun 1k views
6 votes
4 answers
6
A bag has $r$ red balls and $b$ black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and the ball is placed back into the bag along with another ball of the same colour. Note that the number of balls in the bag will ...
asked Feb 18 in Probability Arjun 1.8k views
2 votes
1 answer
7
There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag. The probability that at least two chocolates are identical is __________ $0.3024$ $0.4235$ $0.6976$ $0.8125$
asked Feb 18 in Quantitative Aptitude Arjun 1.7k views
2 votes
2 answers
8
The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter $2$. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to $2$ decimal places) is ____________.
asked Feb 18 in Probability Arjun 1.1k views
1 vote
1 answer
9
Consider the two statements. $S_1:\quad$ There exist random variables $X$ and $Y$ such that $ \left(\mathbb E[(X-\mathbb E(X))(Y-\mathbb E(Y))]\right)^2>\textsf{Var}[X]\textsf{Var}[Y]$ $S_2:\quad$ For all random variables $X$ ... Both $S_1$ and $S_2$ are true $S_1$ is true, but $S_2$ is false $S_1$ is false, but $S_2$ is true Both $S_1$ and $S_2$ are false
asked Feb 18 in Probability Arjun 791 views
4 votes
2 answers
10
A sender $(\textsf{S})$ transmits a signal, which can be one of the two kinds: $H$ and $L$ with probabilities $0.1$ and $0.9$ respectively, to a receiver $(\textsf{R})$. In the graph below, the weight of edge $(u,v)$ is the probability of receiving $v$ ... $0.7$. If the received signal is $H,$ the probability that the transmitted signal was $H$ (rounded to $2$ decimal places) is __________.
asked Feb 18 in Probability Arjun 795 views
0 votes
0 answers
11
$\text{Description for the following question:}$ If $Z$ is a continuous random variable which follows normal distribution with mean=$0$ and standard deviation=$1$, then $\mathbb{P}(Z\leq a)=\int^a _{-\infty} \frac{\exp\{\frac{-z^2}{2}\}}{\sqrt{2\pi}}dz=\Phi(a), $ where $\Phi(a=-2)=0.02,$ ... less than 0.02 $\int^{18} _{-\infty} \frac{1}{\sqrt{2\pi .2^2}}\exp\{-\frac{1}{2}(\frac{x-24}{2})^2\}dx$
asked Jan 29 in Others soujanyareddy13 98 views
0 votes
0 answers
12
$\text{Description for the following question:}$ If $Z$ is a continuous random variable which follows normal distribution with mean=$0$ and standard deviation=$1$, then $\mathbb{P}(Z\leq a)=\int^a _{-\infty} \frac{\exp\{\frac{-z^2}{2}\}}{\sqrt{2\pi}}dz=\Phi(a), $ where $\Phi(a=-2)=0.02,$ ... more than 0.4 less than 0.5
asked Jan 29 in Others soujanyareddy13 51 views
0 votes
0 answers
13
$\text{Description for the following question:}$ If $Z$ is a continuous random variable which follows normal distribution with mean=$0$ and standard deviation=$1$, then $\mathbb{P}(Z\leq a)=\int^a _{-\infty} \frac{\exp\{\frac{-z^2}{2}\}}{\sqrt{2\pi}}dz=\Phi(a), $ ... will last more than $26$ months approximately equals $16\%$ is more than $15\%$ is less than $14\%$ is between $10\%$ and $15\%$
asked Jan 29 in Others soujanyareddy13 47 views
0 votes
2 answers
14
In an entrance examination with multiple choice questions, with each question having four options and a single correct answer, suppose that only $20\%$ candidates think they know the answer to one difficult question and only half of them know it correctly and the ... tick the same. If a candidate has correctly answered the question, what is the (conditional) probability that she knew the answer?
asked Jan 29 in Others soujanyareddy13 119 views
0 votes
1 answer
15
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. $\text{Description for the following question:}$ Suppose $X$ is the number of successes ... one credit default in a year. You can assume that whether a given debtor will default or not is independent of the behavior of other debtors.
asked Jan 29 in Others soujanyareddy13 36 views
0 votes
1 answer
16
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. $\text{Description for the following question:}$ Suppose $X$ is the number of successes out of ... $\mathbb{E}(X)=np$. For the situation in the previous problem, what is the expected number defaults?
asked Jan 29 in Others soujanyareddy13 39 views
0 votes
1 answer
17
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. $\text{Description for the following question:}$ Suppose $X$ is the number of successes out of $n$ ... on his/her credit than the bank loses the entire loan amount. What is the expected revenue of the bank from a loan of $Rs. 100,000?$
asked Jan 29 in Others soujanyareddy13 33 views
0 votes
1 answer
18
Suppose you roll two six-sided fair dice with faces numbered from $1$ to $6$ and take the sum of the two numbers that turn up. What is the probability that: the sum is $12;$ the sum is $12$, given that the sum is even; the sum is $12$, given that the sum is an even number greater than ... $\frac {1}{14}$, respectively $\frac {1}{36}, \frac {1}{16} $, and $\frac {1}{12}$, respectively
asked Jan 29 in Others soujanyareddy13 40 views
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