1. Assume the probability of being born a boy is the same as being born a girl. Find the probability that a family with children will have the following composition: The oldest two are girls. (Give the fractional answer, before converting to decimal )

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)? 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\( )=0.994 \) (Round to three decimal places as needed.) (c) What value does F approach as \( t \) becomes unbounded in the positive direction? (

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:

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?