Ou roll a fair 666-sided die. What is \text{P(not 5})P(not 5)start text, P, left parenthesis, n, o, t, space, 5, end text, right parenthesis? If necessary, round your answer to 222 decimal places.

Given:

A 6 sided die is rolled.

To find:

The probability of getting not 5, i.e., P( not 5).

Solution:

If a 6 sided die is rolled, then the possible outcomes are 1, 2, 3, 4, 5, 6.

Total outcomes = 6

Favorable outcomes = Possible numbers other than 5 = 5

Now,

Therefore, the probability of getting not 5, i.e., P( not 5) is 0.83.

∠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.

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step-by-step explanation: