Imagine you have m distinct baskets in which you’re throwing n number of balls at random. each throw is independent of any other throw, and every basket is equally as likely to get a ball on a throw. after the n throws, what is the probability that a given basket is empty?

Step-by-step explanation:

Given a basket, the probability of a ball to end there is (because there are m baskets).

Then, the probability of a ball to end in other basket is .

Finally, the probability of the basket to remain empty after n throws is

This last is because, given n independets events with probability p, the probability for all of them to happen is . In this case

∠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: -0.5 would be the most likley outcome

step-by-step explanation: