Question Type 5: Working with conditions Exercises

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

A bag contains 5 red, 3 green, and 2 blue marbles. You draw one marble with replacement and then draw a second. What is the probability of red then green?

A bag contains 3 red and 7 green marbles. You draw one marble without replacement, then draw a second. What is the probability of drawing a red then a green?

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?

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

A bag contains 5 red, 3 green, and 2 blue marbles. You draw one marble without replacement and then draw a second. What is the probability of red then green?

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

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

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

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

Two dice are rolled. What is the probability that the sum is 6 given that at least one die shows a 4?

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