Question Type 6: Working with replacement Exercises

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

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

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

Events $A$ and $B$ satisfy $P(A ∣ B) = 0.4$ and $P(A ∩ B) = 0.08$. Find $P(B)$.

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

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?

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

Events $A$ and $B$ are mutually exclusive with $P(A) = 0.5$ and $P(A \cup B) = 0.7$. Find $P(B)$.

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

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 $p$.

Two fair dice are rolled. Find the probability that both dice show an even number.