Recent questions tagged conditional-probability

Karan tells truth with probability $\dfrac{1}{3}$ and lies with probability $\dfrac{2}{3}.$ Independently, Arjun tells truth with probability $\dfrac{3}{4}$ and lies with...

A drawer contains $2$ Blue, $4$ Red and $2$ Yellow balls. No two balls have the same radius. If two balls are randomly selected from the drawer, what is the probability t...

In a certain town, the probability that it will rain in the afternoon is known to be $0.6$. Moreover, meteorological data indicates that if the temperature at noon is les...

The probability of an event $B$ is $P_1$. The probability that events $A$ and $B$ occur together is $P_2$ while the probability that $A$ and $\bar{B}$ occur together is $...

Let $A$ and $B$ be any two arbitrary events, then, which one of the following is TRUE?$P (A \cap B) = P(A)P(B)$$P (A \cup B) = P(A)+P(B)$$P (A \mid B) = P(A \cap B)P(B)$$...

An automobile plant contracted to buy shock absorbers from two suppliers $ X$ and $ Y$ . $ X$ supplies $60\%$ and Y supplies $40\%$ of the shock absorbers. All shock abso...

If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?$\left(\dfrac{1}{3}\right)$$\le...

Suppose a fair six-sided die is rolled once. If the value on the die is $1, 2,$ or $3,$ the die is rolled a second time. What is the probability that the sum total of val...

Box $P$ has $2$ red balls and $3$ blue balls and box $Q$ has $3$ red balls and $1$ blue ball. A ball is selected as follows: (i) select a box (ii) choose a ball from the ...

Let $P(E)$ denote the probability of the event $E$. Given $P(A) = 1$, $P(B) =\dfrac{1}{2}$, the values of $P(A\mid B)$ and $P(B\mid A)$ respectively are$\left(\dfrac{1}{4...

An unbalanced dice (with $6$ faces, numbered from $1$ to $6$) is thrown. The probability that the face value is odd is $90\%$ of the probability that the face value is ev...

Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next da...