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.
Answer:
C. KN
Step-by-step explanation:
In the line you can see GJ is 3 units and KN is the only answer to be 3 units apart as well. So your answer is C!
Answer:
f(x) = 4x^2 +2,
is the function
Step-by-step explanation:
if i get this wrong imma tie a brick to my feet and jump in the ocean
Answer:
no
Step-by-step explanation:
If this were a right triangle we would assume the Pythagorean Theorem to prove it
this gives us
49+64=84.64
this is 143=84.64 and therefore not equal and not a right triangle
Answer:
Step-by-step explanation:
0.2x+2.7x−8.1 = - 5.2x and 6.9+1.1x = 8
Ig you add them it would be 2.8
