menu
bartleby
search
close search
Hit Return to see all results

An airport limo has 4 passengers and stops at 6 different hotels.  What is the probability that two or more people will be staying at the same hotel?

Question

An airport limo has 4 passengers and stops at 6 different hotels.  What is the probability that two or more people will be staying at the same hotel?

check_circleAnswer
Step 1

Concept of probability:

Probability deals with the likelihood of occurrence of a given event. The probability value lies between 0 and 1. An event with probability 1 is considered as certain event and an event with probability 0 is considered as an impossible event. The probability of 0.5 infers of having equal odds of occurring and not occurring of an event.

The general formula to obtain probability of an event A is,

P(A) = (number of favourable elements for event A)/(Total number of elements in the sample space).

The basic properties of probability are given below:

fullscreen
Step 2

Find the probability that none of the passengers stay in the same hotel:

The total number of hotels is 6.

The number of passengers is 4.

Here, the objective is to find the probability that 2 or more passengers will be staying in the same hotel.

To reach the objective, it is important to find the opposite probability. That is, the probability that every passenger stays in the different hotel (no two or more passengers stays in the same hotel).

Let the 4 passengers be denoted by A, B, C and D.

  • There are 6 different hotels for the passenger A to stay. That is, n(A) = 6.
  • Then, there are 5 different hotels for the passenger B to stay other than the hotel of A. That is, n(B) = 5.
  • Next, there are 4 different hotels for the passenger C to stay other than the hotels of A and B. That is, n(C) = 4.
  • After that, there are 3 different hotels for the passenger D to stay other than the hotels of A, B and C. That is, n(D) = 3.

The total number of hotels is n(S) = 6.

The probability that none of the passengers stay in the same hotel is obtained as (5/18) from the calculation given below:

fullscreen
Step 3

Find the probability that two or more passenger’s will be staying in the same hotel:

The two or more passenger’...

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Math

Probability

Related Probability Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: Seven boys and five girls are going to a county fair to ride the teacup ride. Each teacup seats four...

A: Total number of possible arrangements:There are 12 seats in the ride. The number of people going for...

question_answer

Q: Which statement is not true for a binomial distribution with n = 10 and p = 1/20 ?a) The mean equal...

A: Given that a binomial distribution with n = 10 and p =1/20.This indicates that there are total of n ...

question_answer

Q: What would be an example of an exposure ratio threshold?

A: Exposure ratio is relevant in a case control study. It involves the following concepts:1)case group ...

question_answer

Q: A diagnostic test for disease X correctly identifies the disease 93% of the time . False positives o...

A: Given thatProbability of disease P(D) = 0.0209Probability that a  diagnosis test identifies disease ...

question_answer

Q: In testing a new drug, researchers found that 3% of all patients using it will have a mild side effe...

A: Introduction to binomial distribution:Consider a random experiment involving n independent trials, s...

question_answer

Q: Hello, Please help me navigate this because I don't even know how tostart answering these questions ...

A: Hello there! I see that there are more number of questions on this graph. I can only help with first...

question_answer

Q: Recall that we say that a random variable X is in the vector space L^2 if it has finite second momen...

A: Properties of a norm:In order to prove that ||X||2 = √E(X2) is a norm, it must satisfy 3 conditions:...

question_answer

Q: The method of tree ring dating gave the following years A.D. for an archaeological excavation site. ...

A: (a) Computation of sample mean and sample standard deviation:The number of samples, n = 9. Using cal...

question_answer

Q: A patient is a member of a health plan that has a 20 percent discount from the provider and a 15 per...

A: According to this question, a patient is a member of a health plan and as per the plan patient will ...

Sorry about that. What wasn’t helpful?