Question

Must show all needed steps in getting to your final answer. And, express your final answer as a decimal.

Show every step NEATLY please

NEATLY AND VERY CLEAR AND READABLE

PLEASE TYPE ANSWER AND WORK

NEATLY AND VERY CLEAR AND READABLE

PLEASE TYPE ANSWER AND WORK

Part 1) Suppose that you are planning to travel a certain air route via plane once each week for your new job. Also, assume that there is a 3% chance that your outbound flight may be cancelled on any given week due to various issues. How many consecutive outbound weekly flights can you fly before the probability of another successful flight (that is, a flight that is not cancelled) drops to 50% or less?

Part 2) Assume that you are playing a game in which you pull a lever and a light comes on. The light will be either red or green. Assume that on any given pull of the lever, P(Red Light) = .40 and P(Green Light) = .60. Find the probability that in pulling the lever 5 times that you will get your 3rd Green Light on the 5th pull of the lever.

Part 3) Suppose in front of you are three boxes that look identical. Further, you are told that one box contains two $1 bills, one contains two $100 bills, and one contains one $1 bill and one $100 bill. You are permitted to choose one box. Then you are asked to remove one bill from the box you chose without looking at the other bill in that box. Suppose that a $100 bill comes out. What is the probability that the other bill in that box is $100?

Answer 1

part 1) Suppose that you are planning to travel a certain air route via plane once each week for your new job. Also, assume that there is a 3% chance that your outbound flight may be cancelled on any given week due to various issues. How many consecutive outbound weekly flights can you fly before the probability of another successful flight (that is, a flight that is not cancelled) drops to 50% or less?

solution:

let number of flights is -------------->n

P(of n successful flights) = (0.97)n <0.5

taking log on both sides n>= 22.75

therefore number of flights before the probability of another successful flight

(that is, a flight that is not cancelled)

drops to 50% or less n=23

please try 22 ; if we require the flight till this probability is more them 0.5)

part-2)Assume that you are playing a game in which you pull a lever and a light comes on. The light will be either red or green. Assume that on any given pull of the lever, P(Red Light) = .40 and P(Green Light) = .60. Find the probability that in pulling the lever 5 times that you will get your 3rd Green Light on the 5th pull of the lever.

solution:

here from negative binomial distribution:

probability that in pulling the lever 5 times that you will get your 3rd Green Light on the 5th pull of the lever

=P(exactly 2 green light on 4 lever and 3rd green light on 5th pull of liver)

=4C2(0.6)3(0.4)2 =0.2074

part-3)Suppose in front of you are three boxes that look identical. Further, you are told that one box contains two $1 bills, one contains two $100 bills, and one contains one $1 bill and one $100 bill. You are permitted to choose one box. Then you are asked to remove one bill from the box you chose without looking at the other bill in that box. Suppose that a $100 bill comes out. What is the probability that the other bill in that box is $100?

solution:

P(Both $1 bill box) = P(One $1 bill and one $100 bill box) = P(Both $100 bill box) = 1/3

P($100 bill | $1 bill box) = 0

P($100 bill | $1 and $100 bill box) = 1/2

P($100 bill | $100 bill box) = 1

Hence by Baye's theorem:

P($100 bill box | $100 bill)

1 *1/3 0 1/3 1/2*1/3+1*1/3

= 2/3