Asurvey is being conducted in a city of 1000, 000 residents. for that purpose, a random sample of size 1000 is chosen. the survey is conducted by choosing people one at a time, with replacement and with equal probabilities. estimate the probability that at least one person is chosen more than once.

Probability that at least one person is chosen more than once is 999/1000

Step-by-step explanation:

Probability is given by number of possible outcomes ÷ number of total outcomes

Probability that at least one person is chosen once is 1/1000

Probability that at least one person is chosen more than once is 1 - 1/1000 = 999/1000

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

answer: 5

step-by-step explanation: