Hello, LArchambeau3!

In both problems, the probability of the second eventon the first event.depends

There are two cases to consider:1. Hannah picks two cards from a bowl with 3 orange, 4 purple, and 3 white cards.

She does not return them to the bowl after picking them.

Find P(the 1st card is not orange and the 2nd card is not white).

. . [1] The first card is white and the second is not white.

. . [2] The first card is purple and the second is not white.

[1] First is White, second is not-White.

. .

. . Now there are: 3 Orange, 4 Purple, and 2 White in the bowl.

. .

. . Hence: .

[2] First is Purple, second is not-White.

. .

. . Now there are: 3 Orange, 3 Purple, 3 White in the bowl.

. .

. . Hence: .

Therefore: .

There are two cases to consider:2. What is the probability that you draw a Heart from a deck of 52 cards,

don't replace it, and then draw an Ace?

. . [1] The first card is the Ace of Hearts.

. . [2] The first card is some other Heart.

[1] The first card is the Ace of Hearts, the second is another Ace.

. .

. . There are 51 card left, 3 of them are Aces.

. .

. . Hence: .

[2] The first card is some other heart, the second is an Ace.

. .

. . There are 51 cards left, 4 of them are Aces.

. .

. . Hence: .

Therefore: .