A person trying to gain access to a bank vault must pass through a series of three security doors. If an attempt to pass through a door is a failure, then the person will not make any further attempts. Let P denote a successful pass and F denote a failed pass. What is the sample space for this random experiment

Sample space is

Step-by-step explanation:

Number of security doors = 3

Let P denote a successful pass and F denote a failed pass.

Sample space refers to a set of all possible outcomes.

If the first attempt to pass through a door is a failure, then the outcome is F.

If the second attempt to pass through a door is a failure, then the outcome is PF.

If the third attempt to pass through a door is a failure, then the outcome is PPF.

If the fourth attempt to pass through a door is a failure, then the outcome is PPP.

Sample space is

∠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.