5 A card is drawn from a standard pack of 52 playing cards. If an Ace is drawn, \( € 20 \) is won; if a picture card is drawn, \( € 4 \) is won. If costs \( € 2 \) to draw a card. Only one prize may be won. Is it worthwhile to play this game? Explain your answer with reference to the expected value.

What does it mean for two events to be independent in probability?

Suppose \( A \) and \( B \) are dependent events. If \( P(A)=0.5 \) and \( P(B \mid A)=0.6 \), what is \( P(A \cap B) \) ? A. 0.5 B. 0.3 C. 0.6 D. 0.1

In a certain Algebra 2 class of 24 students, 9 of them play basketball and 5 of them play baseball. There are 3 students who play both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball?

A basketball player makes \( 70 \% \) of his free throws. If he attempts 20 free throws, what is the probability that he makes at least 15 of them? (Hint: this is a binomial distribution problem with the following parameters: \( n=20 \) as the number of trials and \( p=0.7 \) as the probability of success on a single trial) a. 0.5122 b. 0.3455 c. 0.416 d. 0.1055

here is a spinner with 15 equal areas, numbered 1 through 15 . If the spinner is spun one time, hat is the probability that the result is a multiple of 3 and a multiple of 4 ?