You play two games against the same oppo- nent. The probability you win the first game is 0.4. If you win the first game, the probability you also win the sec- ond is 0.2. If you lose the first game, the probability that you win the second is 0.3.a) Are the two games independent? Explain. b) What's the probability you lose both games? c) What' s the probability you win both games? d) Let random variable X be the number of games you win. Find the probability model for X. e) What are the expected value and standard

∠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.

the answer is c hope it

step-by-step explanation:

step-by-step explanation: