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.

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.)

Pass Completions Football player Peyton Manning completes a pass \( 64.8 \% \) of the time. Find the probability that (a) the first pass Peyton completes is the second pass, (b) the first pass Peyton completes is the first or second pass, and (c) Peyton does not complete his first two passes. (Source: National Football League)

A high-yield string bean plant will produce, on average, at least 30 beans per week. Of 639 bean plants in a greenhouse, 426 plants produced less than 30 beans per week. What is the approximate probability that a randomly selected string bean plant will be a high-yield plant?

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 \( \square \) minutes are needed for the probability to reach \( 90 \% \). (Round to two decimal places as needed.)