Just need confirmation for my answers ! Thank you!
1. The chance that the top card in a well shuffed deck is a two or a nine is:
8/52 = 15.4% (4 twos and 4 nines in deck)
2. The chance that the eighth card from the top of the deck is a heart or a diamond is:
26/52 = 50% (13 hearts & 13 diamonds in deck); assuming we don't know the first 7 cards; the position doesn't matter here.
3. The chance that the top card in the deck is a two or a nine given that the eighth card from the top is a heart or a diamond is:
Wouldn't it still be 15.4%? Unless they mention that the eighth card is a two or a nine, it wouldn't matter right?
4. Are the events that the top card is a two or a nine and that the eighth card is a heart or a diamond independent?
Yes (I'm not sure entirely on this one. An explanation would be great! Other options: No or Cannot Determined Without Knowing The Other Cards)
Thanks a bunch!