You pick a card at random. Without putting the first card back, you pick a second card at random. What is the probability of picking a 7 and then picking a number greater than 8 ? Simplify your answer and write it as a fraction or whole number.

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?

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

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

A widget company produces 25 widgets a day, 5 of which are defective. Find the probability of selecting 5 widgets from the 25 produced where none are defective. A. \( \frac{2584}{8855} \) B. \( \frac{1}{5} \) C. \( \frac{1}{3125} \) D. \( \frac{1}{10626} \)

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