Question Type 6: Working with replacement Exercises

A fair coin is tossed twice. What is the probability of getting at least one head?

A spinner is divided into 8 equal regions numbered 1 through 8. What is the probability of landing on a number divisible by 3?

Two fair dice are rolled. What is the probability that both dice show an even number?

Two fair six-sided dice are rolled. What is the probability that the sum of the numbers is 7?

Events A and B are mutually exclusive with $P(A)=0.5$ and $P(A\text{ or }B)=0.7$. Find $P(B)$.

A standard deck of 52 cards is shuffled and one card is drawn, then without replacement a second card is drawn. What is the probability the first card is red and the second is black?

An urn contains 5 red and 7 blue balls. Three balls are drawn one after another without replacement. What is the probability that exactly two of the drawn balls are red?

Events A and B satisfy $P(A\mid B)=0.4$ and $P(A\cap B)=0.08$. Find $P(B)$.

A biased coin has probability $p$ of landing heads. It is tossed twice. Given that the probability of exactly one head is 0.48, find all possible values of $p$.

Events A, B, C form a partition of the sample space with $P(A)=0.2$, $P(B)=0.3$, and $P(C)=0.5$. Given $P(D\mid A)=0.1$, $P(D\mid B)=0.2$, and $P(D\mid C)=0.4$, find $P(D)$ using the law of total probability.

Two fair dice are rolled. Given that the sum is greater than 8, what is the probability that the sum is 11?