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
aleksley [76]
3 years ago
12

What is the probability of these events when we randomly select a permutation of {1,2, ..., n} where n≥4? a) 1 precedes 2 c) 1 i

mmediately precedes 2 d) n precedes 1 and n−1 precedes 2
Mathematics
1 answer:
Paraphin [41]3 years ago
3 0

Answer:

a) 1/2

b) 1/n

c) 1/4

Step-by-step explanation:

a) For each permutation, either 1 precedes 2 or 2 precedes 1. For each permutation in which 1 precedes 2, we can swap 1 and 2 to obtain a permutation in which 2 preceds 1. Thus, half of the total permutations will involve in 1 preceding 2, hence, the probability for a permutation having 1 before 2 is 1/2.

c) If 2 is at the start of the permutation, then it is impossible for 1 to be before 2. If that is not the case, then 1 has a probability of 1/n-1 to be exactly in the position before 2. We can divide in 2 cases using the theorem of total probability,

P( 1 immediately preceds 2) = P (1 immediately precedes 2 | 2 is at position 1) * P(2 is at position 1) + P(1 immediately precedes 2 | 2 is not at position 1) * P(2 is not at position 1) = 0 * 1/n + (1/n-1)*(n-1/n) = 1/n.

d) We can divide the total of permutations in 4 different groups with equal cardinality:

  • Those in which n precedes 1 and n-1 precedes 2
  • those in which n precedes 1 and 2 precedes n-1
  • those in which 1 precedes n and n-1 precedes 2
  • those in which 1 precedes n and 2 precedes n-1

All this groups have equal cardinality because we can obtain any element from one group from another by making a permutations between 1 and n and/or 2 and n-1.

This means that the total amount of favourable cases (elements of the first group) are a quarter of the total, hence, the probability of the event is 1/4.

You might be interested in
PLLLLLEEEEAAAASSSSEEEEEEEE HEEEEEELLLLP MMEEEEEEEEEEEE WILL AWARD BRAINLIEST IF HELPED
RSB [31]
It’s a cool shape. Reminds me a flash.
4 0
3 years ago
Read 2 more answers
What is the smallest unit of measurement?
kvasek [131]
The smallest unit of measure is the millimeter

Hope this helps ;)
3 0
3 years ago
Read 2 more answers
If a litre of water is provided for 20 people, how much for 50 people?
Vinvika [58]


2 1/2 litres would be a reasonable amount of water assuming everyone drinks the same amount.


7 0
3 years ago
Read 2 more answers
How do the prefixes in the metric system relate to the basic units?
WITCHER [35]
The basic unit of length in the metric system is the meter. Grams are used to measure weight and liter is used to measure liquid capacity
besides, it is used  so that you can express very large and very small numbers in a short unambiguous manner.
Example Instead of saying "three thousand million" meters
They classify the decimal place of the basic unit. ie, the meter is classified with milli (1/1000), centi(1/100), deci (1/10), Deca (10), Hecto (100), Kilo (1000).
4 0
3 years ago
Read 2 more answers
4.2 using similar shapes​
aksik [14]

Answer:

Nininininiji

Step-by-step explanation:

6 0
2 years ago
Other questions:
  • What times what is equals 455 in prime numbers
    9·1 answer
  • Analyzing Dialogue
    13·2 answers
  • Calculate the average daily balance, finance charge, and new balance using the average daily balance method.
    8·1 answer
  • Maël mixes 151515 milliliters (\text{mL})(mL)left parenthesis, start text, m, L, end text, right parenthesis of bleach with 3.75
    14·1 answer
  • Brainliest badge you help me no kizzy
    10·2 answers
  • Jason has a total of 15 coins which are dimes and nickels. The coins are worth $1.10. How many dimes does he have?
    9·1 answer
  • If the neighborhood holds 13 total games and all 50 athletes participate, how many 6-player games and how many 2-player games ar
    7·1 answer
  • Im doing my final. Answer and you get whatever you want.
    15·1 answer
  • ASAP!!! I NEED HELP geometry/trigonometry please
    13·1 answer
  • 2/3 question. all who answer get respect. even if inncorrect
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!