Recent questions tagged probability

A box contains three apples and two oranges. Two fruits are removed randomly in succession. The probability that the first is an apple and the second is an orange is $\_\...

Indian Premier League has divided the sixteen cricket teams into two equal pools: Pool-A and Pool-B. Four teams of Pool-A have blue logo jerseys while the rest four have ...

A random variable $X$ has a probability density function$$f_{X}(x)=\begin{cases} e^{-x}, & x \geq 0 \\ 0, & \text { otherwise } \end{cases}$$The probability of $X>2$ is $...

A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and third balls drawn are re...

A game consists of spinning an arrow around a stationary disk as shown below. When the arrow comes to rest, there are eight equally likely outcomes. It could come to rest...

Consider that $\text{X}$ and $\text{Y}$ are independent continuous valued random variables with uniform $\text{PDF}$ given by $X\sim U\left ( 2,3 \right )$ and $Y\sim U\l...

Consider two identical bags $B1$ and $B2$ each containing $10$ balls of identical shapes and sizes. Bag $B1$ contains $7$ Red and $3$ Green balls, while bag $B2$ contains...

A player throws a ball at a basket kept at a distance. The probability that the ball falls into the basket in a single attempt is 0.1. The player attempts to throw the ba...

Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is$\frac{1}{9}$$\frac{2}{9}...

A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and...

The function p(x) is given by p(x) = A/x$^\mu$ where A and $\mu$ are constants with $\mu$ 1 and 1 $\le$ x <$\infty$ and p(x) = 0 for -$\infty$ < x <1. For p(x) to be a ...

An urn contains $5$ red and $7$ green balls. A ball is drawn at random and its color is noted. The ball is placed back into the urn along with another ball of the same co...

A coin is tossed thrice. Let $X$ be the event that head occurs in each of the first two tosses. Let $Y$ be the event that a tail occurs on the third toss. Let $Z$ be the ...

The probability that a thermistor randomly picked up from a production unit is defective is $0.1$. The probability that out of $10$ thermistors randomly picked up, $3$ ar...

The probability density function of a random variable $X$ is $P_X(x)=e^{-x}$ for $x\underline{>} 0$ and $0$ otherwise. The expected value of the function $g_X(x)=e^{3x/4}...

$10\%$ of the population in a town is $HIV^+$. A new diagnostic kit for $HIV$ detection is available; this kit correctly identifies $HIV^+$ individuals $95\%$ of the time...

Given that $x$ is a random variable in the range $[0,\infty]$ with a probability density function $\frac{e \frac{-x}{2}}{K}$, the value of the constant $K$ is __________.

What is the chance that a leap year, selected at random, will contain $53$ Saturdays?$2/7$$3/7$$1/7$$5/7$

A continuous random variable $X$ has a probability density function $f(x)=e^{-x}, 0<x<\propto$. Then $\text{P{X>1}}$ is $0.368$$0.5$$0.632$$1.0$

$\text{A}$ and $\text{B}$ are friends. They decide to meet between $\text{1 PM}$ and $\text{2 PM}$ on a given day. There is a condition that whoever arrives first will no...

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is$1/3$$1/2$$2/3$$3/4$

Two independent random variables $\text{X}$ and $\text{Y}$ are uniformly distributed in the interval $[-1, 1]$. The probability that max$\text{[X, Y]}$ is less than $1/2$...

Two bags A and B have equal number of balls. Bag A has 20% red balls and 80% green balls. Bag B has 30% red balls,60% green balls and 10% yellow balls. Contents of Bags A...

Consider a sequence of tossing of a fair coin where the outcomes of tosses are independent. The probability of getting the head for the third time in the fifth toss is$\f...

X and Y are two independent random variables with variances 1 and 2, respectively. Let Z = X – Y. The variance of Z is0123