Amy and Samiha have a hat that contains two playing cards, one ace and one king. They are playing a game where they randomly select a card out of the hat four times, with replacement.
Samiha thinks that the probability of getting either an ace or a king on the first pick is greater than the probability of getting at least one ace in the four picks. Amy disagrees. She thinks that the two probabilities are equal.
The sample space of possible outcomes is listed below. A represents an ace, and K represents a king.
**Who is correct, Amy or Samiha?**
[[☃ radio 1]]
| | | |
- | - | - | - |
AAAA | AAAK | KKAK | AKKA
KAAA | KKKK | KKKA | KKAA
AKAA | AKKK | AAKK | KAKA
AAKA | KAKK | AKAK |KAAK