Question 7 ( 0 points) In a certain state's lottery, 48 balls numbered 1 through 48 are placed in a machine and six of them are drawn at random. If the six numbers drawn match the numbers that a player had chosen, the player wins \( \$ 1,000,000 \). In this lottery, the order the numbers are drawn in doesn't matter. Compute the probability that you win the million-dollar prize if you purchase a single lottery ticket. Show all of the 0 's and then two actual significant digits.

1. Indica el espacio muestral para los siguientes eventos. A. Lanza un dado dos veces y observa la suma de puntos de sus caras. B. Lanza un dado dos veces y observa la diferencia de puntos de sus caras. C. Lanza una moneda y un dado, ¿cuáles son los resultados posibles?

Between 12:00 PM and 1:00 PM, cars arrive at a bank's drive-thru at the rate of 18 cars per hour ( 0.3 car per minute). The following formula from statistics can be used to determine the probability that a car will arrive within \( t \) minutes of 12:00 PM. Complete parts (a)-(c). F(t) \( =1-e^{-0.3 t} \) (a) Determine how many minutes are needed for the probability to reach 30\%. About \( \square \) minutes are needed for the probability to reach 30\%. (Round to two decimal places as needed.)

Between 12:00 PM and 1:00 PM, cars arrive at a local bank's drive-thru at the rate of 8 cars per hour ( 0.13 car per minute). The formula below from probability can be used to determine the probability that a car will arrive within t minutes of 12:00 PM. Use this information to answer the questions given below in parts (a)-(e). F(t) \( =1-e^{-0.13 t} \) (a) What is the probability that a car will arrive within 35 minutes of \( 12: 00 \) PM (that is, before 12:35 PM)? \( \mathrm{F}(35)=0.989 \) (Round to three decimal places as needed.) (b) What is the probability that a car will arrive within 40 minutes of \( 12: 00 \) PM (that is, before 12:40 PM)? F(40) \( =\square \) (Round to three decimal places as needed.)

Between 12:00 PM and 1:00 PM, cars arrive at a bank's drive-thru at the rate of 18 cars per hour ( 0.3 car per minute). The following formula from statistics can be used to determine the probability that a car will arrive within t minutes of 12:00 PM. Complete parts (a)-(c). F(t) \( =1-e^{-0.3 t} \) (a) Determine how many minutes are needed for the probability to reach 30\%. About 1.19 minutes are needed for the probability to reach \( 30 \% \). (Round to two decimal places as needed.) (b) Determine how many minutes are needed for the probability to reach \( 90 \% \). About 7.68 minutes are needed for the probability to reach \( 90 \% \). (Round to two decimal places as needed.) (c) Is it possible for the probability to equal \( 100 \% \) ? Explain. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. Yes, about \( \square \) minutes are needed for the probability to B. No, because when determining the number of minutes, the (Round to two decimal places as needed.)

Major Hurricanes A major hurricane is a hurricane with wind speeds of 111 miles per hour or greater. During the 20th century, the mean number of major hurricanes to strike the U.S. mainland per year was about 0.6 . Find the probability that in a given year (a) exactly one major hurricane strikes the U.S. mainland, (b) at most one major hurricane strikes the U.S. mainland, and (c) more than one major hurricane strikes the U.S. mainland. (Source: