17 On considère deux événements \( A \) et \( B \) tels que \( P(A)=0,3, P(A \cap B)=0,2 \) et \( P(B)=0,6 \). Calculer \( P(A \cup B), P_{B}(A) \) et \( P_{A}(B) \).

logía, Química, Física y Lenguaje. Si se toma uno de ellos, ¿cuá a probabilidad de que este sea de matemática o de física? \( 1 / 5 \) b) \( 3 / 5 \) c) \( 2 / 5 \mathrm{~d} / 4 / 5 \)

The expected value of betting \( \$ 1 \) on one roulette number is approximately \( -\$ .05 \). What does this mean in practical terms? If many people made this bet over the course of the night, the house would expect to take in approximately a \( 5 \% \) return. If I bet \( \$ 1 \) one time, I would expect to leave the table with approximately 95 cents. I am almost guaranteed to lose this bet I am almost guaranteed to win this bet

4 Permutations and Probabilities: 20 pts, Part A: 10 pts. You are tasked with organizing a group of 6 people: Allice, Bob, Charlie, David, Eva, and Frank. How many different ways can you arrange these 6 people in a line? Show your work to receive full credit. Part B: 10 pts. If the arrangement from Part A must have Alice and Bob standing next to each other, what is the probability that Alice and Bob will be next to each other in a random arrangement? Show your work to receive full credit.

3. A six-sided die is rolled one time. Find the probability of getting an even number greater than 2 .

After a particular surgery, patients are placed in an intensive care unit (ICU) until their condition stabilizes. Then they are transferred to a special care ward (SCW), where they remain until they are released from the hospital. In a particular metropolitan area, a study of hospital records produced the following data: each day \( 2 \% \) of the patients in the ICU died, \( 49 \% \) were transferred to the SCW, and the remainder stayed in the ICU. Furthermore, each day \( 3 \% \) of the patients in the SCW developed complications and were returned to the ICU, \( 1 \% \) died while in the SCW, \( 22 \% \) were released from the hospital, and the remainder stayed in the SCW. A) In the long run, what percentage of the patients in the ICU are released from the hospital? \( 91.43 \% \) (Round to two decimal places as needed.) B) In the long run, what percentage of the patients in the SCW die without ever being released from the hospital? \( \square \% \) (Round to two decimal places as needed.)