(7) A fair, standard die is rolled and the winnings for each outcome are as follows: Roll a 6: Win \( € 5 \) Roll a 3: Win \( € 1 \) Roll any other number. Win nothing (a) Calculate the expected value for this game. It is then decided to charge \( € 1.50 \) per game. (b) Calculate the expected value (net of the \( € 1.50 \) charge) for this game.

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

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

Some red, white, and blue candies were placed in a bowl. Some contain nuts, and some do not. Suppose one of the candies were chosen randomly from all the candies in the bowl. Which of the following represents a conditional probability? A. The probability that the candy is blue B. The probability that the candy is not red C. The probability that it contains nuts and is white D. The probability that it does not contain any nuts, given that the candy is red

In un'urna ci sono 3 palline rosse e 2 blu. Se estraiamo una pallina rossa, qual è la probabilità di estrarre poi una seconda pallina rossa?