Recent questions and answers in Probability and Statistics

An experiment is performed by rolling an unbiased die once. Events A and B are defined as follows:Event A: The outcome of the rolled die is a prime number.Event B: The ou...

The data given in the table are fitted to the equation $y=m x$ using the method of least squares. The value of $m$ is $\_\_\_\_$ (rounded off to one decimal place).\[\beg...

​​​​A box contains $3$ identical green balls and $7$ identical blue balls. Two balls are randomly drawn without replacement from the box. The probability of drawing $1$ g...

An exhibition was held in a hall on $15$ August $2022$ between $\text{3 PM}$ and $\text{4 PM}$ during which any person was allowed to enter only once. Visitors who entere...

A source placed at the origin of a circular sample holder (radius $r=1 \: m$) emits particles uniformly in all directions. A detector of length $l=1 \: cm$ has been place...

The probability distribution function of a random variable $X$ is shown in the following figure.From this distribution, random samples with sample size $n=68$ are taken. ...

In a box, there are $5$ green balls and $10$ blue balls. A person picks $6$ balls randomly. The probability that the person has picked $4$ green balls and $2$ blue balls ...

Two unbiased dice are thrown. Each dice can show any number between $1$ and $6$. The probability that the sum of the outcomes of the two dice is divisible by $4$ is _____...

The marks obtained by a set of students are: $38,\:84,\:45,\:70,\:75,\:60,\;48$.The mean and median marks, respectively, are$45$ and $75$$55$ and $48$$60$ and $60$$60$ an...

A box has $6$ red balls and $4$ white balls. A ball is picked at random and replaced in the box, after which a second ball is picked.The probability of both the balls bei...

The diameters of sand particles in a sample range from $50$ to $150$ microns. The number of particles of diameter x in the sample is proportional to $\frac{1}{50+x}$. The...

In rolling of two fair dice, the outcome of an experiments is considered to be the sum of the numbers appearing on the dice. The probability is highest for the outcome of...

Consider the following two normal distributions$f_{1}\left ( x \right )=exp\left ( -\pi x^{2} \right )$$f_{2}\left ( x \right )=\frac{1}{2 \pi}exp\left \{ -\frac{1}{4\pi ...

For two rolls of a fair die, the probability of getting a 4 in the first roll and a number less than 4 in the second roll, up to 3 digits after the decimal point, is ____...

The number of emails received on six consecutive days is 11, 9, 18, 18, 4 and 15,respectively.what are the median and the mode for these data?18 and 11, respectively13 an...

A box containing $10$ identical components has $6$ red balls and $2$ blue balls. If each compartment can hold only one ball, then the number of different possible arrange...

A watch uses two electronic circuits ($ECs$). Each $EC$ has a failure probability of $0.1$ in one year of operation. Both $ECs$ are required for functioning of the watch....