Two experiments are to be performed. the first can result in any one of m possible outcomes. if the first experiment results in outcome i, then the second experiment can result in any of ni possible outcomes, i = 1, 2, . . , m. what is the number of possible outcomes of the two experiments

The first experiment has M probabilities, and the second has I(m) outcomes, that depends on the result of the first.

And lets call m to the result of the first experiment.

If the outcome of the first experiment is 1, then the second experiment has 1 possible outcome.

If the outcome of the first experiment is 2, then the second experiment has 2 possibles outcomes.

If the outcome of the first experiment is M, then the second experiment has M possibles outcomes.

And so on.

So the total number of combinations C is the sum of all the cases, where we exami

1 outcome for m = 1

+

2 outcomes for m=2

+

.

.

.

+

M outcomes for m = M

C = 1 + 2 + 3 + 4 +...´+M

∠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.