Probability

Two cards are drawn one after another without replacement from a well-shuffled pack of $52$ cards. What is the probability that both the cards drawn are aces?

Given that $P(A) = 0.8$, $P(B) = 0.5$, and $P(B|A) = 0.4$, find the value of $P(A \cap B)$.

If $A$ and $B$ are two independent events such that $P(A) = 0.3$ and $P(B) = 0.4$, what is the value of $P(A \cap B)$?

If $P(A) = 0.25$ and $P(B) = 0.2$ are independent events, find $P(A \cap B)$.

A bag contains 3 green and 4 yellow balls. Two balls are drawn with replacement. What is the probability that the first is green and the second is yellow?

If $P(A) = 0.3$ and $P(B) = 0.3$ are independent, find $P(A \cup B)$.

Box A contains $10$ bulbs of which $2$ are defective. Box B contains $10$ bulbs of which $1$ is defective. A box is chosen at random and a bulb is drawn. What is the probability the bulb is defective?

A die is rolled. If the number is even, Bag 1 ($3$ white, $2$ black) is chosen. If the number is odd, Bag 2 ($2$ white, $3$ black) is chosen. What is the probability of drawing a white ball?

Employee A handles $40\%$ of the files with an error rate of $1\%$. Employee B handles $60\%$ with an error rate of $2\%$. If an error is found, what is the probability it was caused by Employee B?

If $E(X) = 4$, then $E(2X+3)$ is:

In a Binomial distribution, if $p=q$, then the value of $p$ is:

For a random variable $X$, $E(X^2) - [E(X)]^2$ calculates the:

If $E(X) = 7$ and $Var(X) = 0$, what is $P(X=7)$?

Which of the following is the correct formula for $Var(X)$?

If a random variable $X$ takes values $a$ and $b$ with probability $0.5$ each, what is the mean of $X$?