Question

In: Statistics and Probability

Suppose that 8 Secret Agents are gathered together in a secret room and that 2 of...

Suppose that 8 Secret Agents are gathered together in a secret room and that 2 of the agents are "double-agents" (they also work for another spy agency). If 4 agents are selected for a special, top-secret mission, what is the probability that a double-agent (at least one) is selected for the mission?

Solutions

Expert Solution

Number of secret agents in a secret room = 8

Number of double agents in the room = 2

Number of non-double agents in the room = 8-2 =6

Number of agents selected for a special, top secret mission = 4

Event of selecting at least one double-agent is selected

= Event of exactly one double-agent is selected and three non-double agents are selected OR

Event of both the double-agents are selected and two non-double agents are selected

Probability that a double-agent (at least one) is selected for the mission

= Probability of exactly one double-agent is selected and three non-double agents are selected +

Probability of both the double-agents are selected and two non-double agents are selected

Probability of exactly one double-agent is selected and three non-double agents are selected

= Number of ways of selecting 1 double agent from 2 double agents x Number of ways of selecting 3 non-double agents from 6 non-double agents / Number of ways of selecting 4 agents from 8 agents

Probability of exactly one double-agent is selected and three non-double agents are selected = 4/7

Probability of both the double-agents are selected and two non-double agents are selected

= Number of ways of selecting 2 double agent from 2 double agents x Number of ways of selecting 2 non-double agents from 6 non-double agents / Number of ways of selecting 4 agents from 10 agents

Probability of both the double-agents are selected and two non-double agents are selected = 3/14

Probability that a double-agent (at least one) is selected for the mission

= Probability of exactly one double-agent is selected and three non-double agents are selected +

Probability of both the double-agents are selected and two non-double agents are selected

= (4/7) + (3/14) = 11/14

Probability that a double-agent (at least one) is selected for the mission = 11/14 = 0.785714286

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Suppose n unrelated families (deﬁned as the husband, the wife, and one child) are gathered together....

Suppose n unrelated families (deﬁned as the husband, the wife, and one child) are gathered together. What is the smallest n for which chances are > 50% that there will be two or more families completely matched in birthdays (i.e., the two husbands have the same birthday, so do the two wives, and so do the two children)?

A family, of Cuban heritage, is gathered in the waiting room waiting to visit their ill...

A family, of Cuban heritage, is gathered in the waiting room waiting to visit their ill family member in the hospital. The family member‘s voices are loud and they are gesturing in a very animated nature. A healthcare provider enters the space and asks to speak to the patient’s spouse. The healthcare provider asks the spouse “Is everything okay? I notice you all seem upset or angry?” What assumption is being made by the healthcare provider? How might you have...

A student is doing some research on the importance of agents used in the laboratory room...

A student is doing some research on the importance of agents used in the laboratory room to kill certain prokaryotes and eukaryotes. Can you list the six different agents and what each specializes for?

Problems: 1. Consider the following situation: 100 people are gathered in a room and 50 of...

Problems: 1. Consider the following situation: 100 people are gathered in a room and 50 of them are selected at random and given a mug, those that were given the mug are asked for the minimum amount of money they would need to give up the mug and those without the mug are asked for the maximum amount they would be prepared to pay for the mug. (a) What does standard theory predict the average amounts written down in each...

The small group gathered in a conference room at a Red Roof Inn near Pittsburgh had...

The small group gathered in a conference room at a Red Roof Inn near Pittsburgh had a common bond and an unusual goal. They all worked for restaurants in the Red Lobster chain. Now they had to figure out whether a Red Lobster waitress had been unjustly fired. The panel included a general manager, an assistant manager, a server, a hostess and a bartender, all of whom had volunteered to review circumstances of the firing and had been told simply...

Question 2 Suppose a researcher gathered survey data from 19 employees and asked the employees to...

Question 2 Suppose a researcher gathered survey data from 19 employees and asked the employees to rate their job satisfaction on a scale from 0 to 100 (with 100 being perfectly satisfied). Suppose the following data represent the results of this survey. Assume that relationship with their supervisor is rated on a scale from 0 to 50 (0 represents a poor relationship and 50 represents an excellent relationship); overall quality of the work environment is rated on a scale from...

Suppose that there are n people in a group, each aware of a diﬀerent secret no...

Suppose that there are n people in a group, each aware of a diﬀerent secret no one else in the group knows about. These people communicate by phone; when two people in the group talk, they share information about all secretes each knows about. For example, on the ﬁrst call, two people share information, so by the end of the call, each of them knows about two secretes. The gossip problem asks for the number of phone calls that are...

Question 2 Suppose there is enough room for a maximum of three (3) cars to park...

Question 2 Suppose there is enough room for a maximum of three (3) cars to park around a fire hydrant. The harm resulting to society rises as additional cars park around the fire hydrant. This is because as more cars park, it becomes more costly for firefighters to navigate their water hoses around the stationary vehicles. The total (not marginal) cost to society as a function of the number of parked cars around a fire hydrant is as follows: Number...

An analyst gathered the following data about stocks J. K. L which together form a value...

An analyst gathered the following data about stocks J. K. L which together form a value weighted index: December 31, Year 1 December 31, Year 2 Stock Price Shares outstanding Price Shares Outstanding J 50 10,000 $60 10,000 K 40 8,000 $30 16,000 L 50 12,000 $40 12,000 Calculate the ending value-weighted index (base index = 100), and briefly explain what it means. Provide your answer up to 2 decimal points.

Suppose that two integers from the set of 8 integers {1, 2, … , 8} are...

Suppose that two integers from the set of 8 integers {1, 2, … , 8} are choosen at random. Find the probability that 5 and 8 are picked. Both numbers match. Sum of the two numbers picked is less than 4. [3+3+4 marks] Suppose that you pick a bit string from the set of all bit strings of length ten. Find the probability that: The bit string has the sum of its digits equal to seven. The bit string has...

Subjects