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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.

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Ivahew [28]

Answer:

add 1/4 to each side

Step-by-step explanation:

x^2+x=11

We take the coefficient of the x term

1

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Then square it

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Add this to both sides of the equation

x^2 + x + 1/4 = 11+1/4

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Arisa [49]

Answer:

The 99% confidence interval for the proportion of readers who would like more coverage of local news is (0.3685, 0.4315).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

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For this problem, we have that:

n = 1600, \pi = 0.4

99% confidence level

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The lower limit of this interval is:

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The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 2.575\sqrt{\frac{0.4*0.6}{1600}} = 0.4315

The 99% confidence interval for the proportion of readers who would like more coverage of local news is (0.3685, 0.4315).

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3 years ago
If pr=5 in and pt=8in what is rs
Nadya [2.5K]
5(5+8)= RS^2
25+40=IRSI^{2}
65= IRSI^{2}
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Hope it helps!
#MissionExam001
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Write me What is 10/12 using simplest form
Serjik [45]
Found it online hope that’s helps

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