Probability

A spinner is divided into $8$ equal sections numbered $1$ to $8$. What is the theoretical probability of landing on an even number?

In a class of $25$ students, $15$ have a pet. What is the relative frequency of students who have a pet?

If you roll a fair six-sided die $600$ times, how many times would you expect to roll a '$4$'?

The probability of entering a correct password on the first try is $0.9$. What is the probability of failing to enter it correctly on two consecutive independent attempts?

A basketball player makes a free throw with probability $0.7$. If they take two independent shots, what is the probability they make exactly one shot?

A bag contains $5$ yellow and $5$ green balls. Two balls are drawn without replacement. What is the probability that they are the same color?

If $P(A') = 0.7$ and $P(B') = 0.8$, and $A$ and $B$ are mutually exclusive, find $P(A \cup B)$.

Two independent events $A$ and $B$ have probabilities $P(A) = \frac{1}{5}$ and $P(B) = \frac{1}{4}$. Find $P(A \cap B)$.

If $P(A) = 0.05, P(B) = 0.15,$ and $P(C) = 0.2$ are mutually exclusive, find $P(A \cup B \cup C)$.

Suppose $P(A) = 0.25$, $P(B) = 0.4$, and $P(A \cap B) = 0.1$. Find $P(A|B)$.

A bag contains 10 marbles: 3 red and 7 blue. Two marbles are drawn without replacement. What is the probability that the second is red, given that the first was red?

If $P(A) = 0.5$ and $P(B|A) = 0.8$, calculate $P(A \cap B)$.