Question Type 5: Working with conditions Exercises

Events $A$ and $B$ are independent with $P(A) = 0.6$ and $P(B) = 0.2$. Find $P(A \cap B)$.

Two fair six-sided dice are rolled. Given that the sum is even, what is the probability that it is larger than 9?

Two dice are rolled. What is the probability that the sum is 8 given that the sum is a composite number?

Events $A$ and $B$ are independent with $P(A) = 0.4$ and $P(B) = 0.21$. Find $P(A \cup B)$.

A bag contains $5$ red, $3$ green, and $2$ blue marbles. A marble is drawn at random and then replaced. A second marble is then drawn at random.

Find the probability that the first marble drawn is red and the second marble drawn is green.

Two fair six-sided dice are rolled. Find the probability that the sum of the dice is 6, given that at least one die shows a 4.

A bag contains 3 red and 7 green marbles. Two marbles are drawn at random, one after the other, without replacement.

Calculate the probability that the first marble drawn is red and the second marble drawn is green.

Two fair dice are rolled. Given that the sum is less than $10$, what is the probability that the sum is divisible by $3$?

Given $P(A \cup B) = 0.7$, $P(A) = 0.5$, and $P(B) = 0.4$, find $P(A \cap B)$.

A bag contains 3 red and 7 green marbles. You draw one marble, replace it, then draw a second marble. What is the probability of drawing a red then a green?

A bag contains 5 red, 3 green, and 2 blue marbles. A marble is drawn at random without replacement and then a second marble is drawn. Find the probability of drawing a red marble followed by a green marble.

Events $A$ and $B$ are mutually exclusive with $P(A) = 0.5$ and $P(B) = 0.3$. Find $P(A ∪ B)$.