You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. find the probability that both cards are black.

Step-by-step explanation:

"AND" means Multiplication, and

"OR" means Addition (in probability)

We want Both cards to be black, that means 1st card black "AND" 2nd card black. So we find individual probabilities and MULTIPLY.

There are 26 black cards from 52 total cards in a normal deck.

P(1st card black) = 26/52 = 1/2

Now, since we HAVEN'T REPLACED, there are now 25 black cards out of 51 total cards. So

P(2nd card black) = 25/51

Now we multiply:

P(both black) =

∠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.

i can't read the graph

step-by-step explanation: