If P(win) = 0.05 for a lottery ticket, what is the probability of not winning?

A computer program randomly generates a digit from $0$ to $9$. What is the sample space for this experiment, and how many possible outcomes are there?

Which of the following is NOT a common notation for the complement of event A?

Which of the following is the correct formal definition of two events being disjoint (mutually exclusive)?

Which of the following statements is correct regarding the relationship between independent and mutually exclusive events?

A consumer feedback agency surveyed $1115$ shoppers to assess their opinions on a new store policy that limits return periods to $7$ days. The summary of responses is shown in the Pareto chart. What is the probability of selecting a shopper who believes the policy is extremely unfair?

Which set notation correctly represents the probability of both event A and event B occurring?

A spinner is spun twice. The first spin lands on red, and the second spin lands on blue. Are the events 'landing on red on the first spin' and 'landing on blue on the second spin' independent or dependent? Explain your reasoning.

A college tracks the number of male and female students who graduate with degrees in science and non-science fields:

What is the probability that a randomly selected science graduate is male?

A coach selects one player for the school team and does not allow that player to be selected again for a relay event. Then a second player is picked from the remaining group. Are these selections independent or dependent? Explain your reasoning.

Let $P\left(G\right)=0.5,P\left(G^{\prime }\right)=0.5,P\left(H\mid G\right)=0.4,$ and $P\left(H\mid G^{\prime }\right)=0.1$. What is $P\left(G\mid H\right)$ according to Bayes’ Theorem?

A company's secure login consists of the employee's department initial, last name initial, and a $3$-digit code. You know the department the employee works in, and you also know that the last digit of the code is even. What is the probability of correctly guessing the employee's login on the first attempt?

A coach needs to assign $7$ runners to specific positions in a relay race. Is this situation best described as a permutation, a combination, or neither?

A school awards ceremony has $12$ students receiving awards. The awards are grouped as follows: $5$ for academic achievement, $2$ for sports, and $5$ for arts. If awards of the same type are indistinguishable, how many different sequences can the awards be presented in?

A box contains $5$ red balls, $3$ blue balls, and $2$ green balls. If $3$ balls are drawn at random without replacement, what is the probability that all three are of different colors?