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.
Quadrant for for number 5
2(5x+7) + 2(8x-9)
= 10x + 14 + 16x - 18
= 26x - 4
Here, ∠1 and ∠2 are complementary angles which means they together are forming a right angle or we can also say that their sum is 90°.So, According to this:
<h3>Now, </h3>
<em>Thus, The measure of m∠1 is 6° and measure of m∠2 is 84°...~</em>
4c + 4t + 3s = total number of legs
example : Lets say u have 3 chairs (c) and 2 tables (t) and 4 stools (s)...
4c + 4t + 3s =
4(3) + 4(2) + 3(4) =
12 + 8 + 12 = 32 legs...then u would have 32 legs
