1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Novosadov [1.4K]
2 years ago
13

Two of the 240 passengers are chosen at random. Find the probability that

Mathematics
1 answer:
hjlf2 years ago
8 0

Step-by-step explanation:

there are in total 240 passengers.

out of these 240, there are 150+30=180 passengers that are in holiday.

and 240-180 = 60 passengers are not.

if we pick one passenger then the probability is 180/240 = 3/4 = 0.75 that he/she is on holiday.

remember : desired "events" over total "events".

i)

now we pick 2 passengers.

the probabilty for the first one to be on holiday is again

3/4 or 0.75.

if that event happens, then we have only 179 passengers out of now 239 to be on holiday.

and to pick one out of that pool to be on holiday is then

179/239 = 0.748953975...

and for both events to happen in one scenario we need to multiply both probabilities (it is an "and" relation, while an addition would be for an "exclusive or" relation).

the probabilty that we pick 2 passengers on holiday is

3/4 × 179/239 = 0.561715481... ≈ 0.5617

we cannot simply square the basic probability of 0.75 (0.75² = 0.5625), because that would mean we pick one passenger, then put him back into the crowd, and then pick a second time (with a chance to pick the same person again). like with rolling a die.

but that is not the scenario as I understand it. it is to pick a passenger, then keep that person singled out and pick a second passenger. hence the difference.

ii)

exactly one of the two is in holiday.

that means

either the first one is on holiday and the second one is not, or the the second one is and the first one is not.

now we model this logic statement in probabilty arithmetic.

please note that after the first pull we need to update the numbers for the remaining pool depending on the result of the first pull.

the total remaining is in both cases 239. but either the remaining people on holiday go down to 179 (and not in holiday stays 60), or the remaining people not on holiday go down to 59 (and on holiday stays 180).

so, the first one is on holiday, and the second one is not :

3/4 × 60/239 (remember : "and" relation)

= 3 × 15/239 = 45/239 = 0.188284519...

the first one is not on holiday, and the second one is :

60/240 × 180/239 = 1/4 × 180/239 = 45/239 =

= 0.188284519...

since there is no overlap of the potential events (there is no event that could be in both cases), this is an exclusive or relation, and we can add the probabilities.

so, the probability for exactly one of the picked passengers to be on holiday is

2×0.188284519... = 0.376569038... ≈ 0.3766

You might be interested in
Yep here we go again:
Shtirlitz [24]

Answer:

9 am it will be IV quadrant

11 it will be I quadrant

hope it helps u

5 0
3 years ago
Read 2 more answers
The dot plot below shows how many laps each student in Coach Toni's gym class ran one day.
Marysya12 [62]
\underbrace{5;5;5;5;10;10;15;15;20;35}_{10}\\\\5\cdot4+10\cdot2+15\cdot2+20+35=125\\\\\frac{125}{10}=12.5\leftarrow\boxed{B}
5 0
3 years ago
Read 2 more answers
Pls help its due soon
slega [8]

Answer:

A

Step-by-step explanation:

If the number of people in the theater must be under 240, then there must be less than 10 seats in each row on the floor to meet fire safety regulations.

if X=10 then, 15 times 10 plus 90 = 240.

Since the number of people must be under 240, there must be less than 10 seats in each row on the floor.

6 0
2 years ago
5-4+7x+1 use the drop down menu
In-s [12.5K]

Answer: 2+7x

Step-by-step explanation:

First you have to do PEMDAS. Then you get this answer.

7 0
3 years ago
Read 2 more answers
The position of an object at time t is given by s(t) = 7 - 14t. Find the instantaneous velocity at t = 7 by finding the derivati
katrin2010 [14]
Given the position function
s(t) = 7 - 14t

The instantaneous velocity is the derivative the the position function:
s'(t) = v = - 14

The velocity in an instant in time is 14 m/s in the opposite direction.
4 0
3 years ago
Read 2 more answers
Other questions:
  • the top ten highest-valued contracts in baseball history are in millions of dollars: 275, 252, 248, 240, 225, 215, 214, 189. 184
    5·1 answer
  • .
    15·2 answers
  • Simplyify (-7)^0 PLEASE HELPP
    15·2 answers
  • HELP ASAP !!!!!!!!!!!!!!!!!! GIVING BRAINLIST
    8·1 answer
  • A rectangle has a perimeter of 44 inches and an area of 72 square inches. what are the lengths of the sides of the rectangle
    8·1 answer
  • Graph ​ y&lt;1−3x ​.<br> Please only answer if you know what you're doing
    11·1 answer
  • An experienced cashier at a grocery store takes 2 seconds to scan each item and 40 seconds to process the customer's payment. 1)
    14·1 answer
  • The value of 4 in 34,258 is how many times the value of 4 in 47,614
    13·1 answer
  • The quantities x and y are proportional. Y 3 30 10 100 16 160 Find the constant of proportionality (r) in the equation y = rx.
    7·2 answers
  • Which is the longer amount? 4/10 of a dollar or 8/10 of a dollar?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!