- Se lanzan dos dados de distunto color ¿Cual es la probabilidad de que sumen 3 o 4 ?

There are 10 people at a meeting and there are 3 different door prizes to give out. How many ways can we select 3 people to receive the door prizes?

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? \( \square \% \) (Round to two decimal places as needed.)

3. Combinations and Probabilities: 20 pts. You are tasked with creating a code using the following three conditions: 1. The code must consist of exactly 4 characters. 2. Each character can be one of the following: A, B, C, or D. 3. The code can repeat characters, but the first character must be different from the last character. How many different codes can you create based on these condi- tions? You MUST show all of your steps to receive full credit.

Question 2 (1 point) Using the definition of probability, what are the chances of pulling a King out of a deck of 52 cards? \( 1 / 52 \) \( 4 / 52 \) \( 8 / 52 \) \( 2 / 52 \)

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.)