Respuesta :
Answer:
The events a) and c) are mutually exclusive.
Step-by-step explanation:
a) This is mutually exclusive, each card has a unique value between 2 and 10, or it is a jack, queen, king, or an Ace. A single card cant have two different values at the same time.
b) This is not mutually exclusive, since you can get a king of clubs. Each card can have any combination of one suit and one value.
c) A face card is either a Jack, a Queen or a King, it is not an Ace. For the same argument of a), a card cant have two different values, therefore this event is mutually exclusive.
d) This is not mutually exclusive, since a card can have any suit independently of the value it has (same argument than b), therefore, a card can be a face card and a spade at the exact time.
Therefore, events a and c are mutually exclusive.
a) Getting a 7 and getting a jack: Mutually exclusive events
b) Getting a club and getting a king: Not mutually exclusive events
c) Getting a face card and getting an ace: Mutually exclusive events
d) Getting a face card and getting a spade: Not mutually exclusive events
A standard deck of cards has 52 cards having 13 ranks each of 4 suites. The 13 ranks are
[tex]\text{Ranks}=\{Ace,2,3,4,5,6,7,8,9,10,Jack,Queen,King\}[/tex]
and the suites are
[tex]Suites=\{Clubs,Diamonds,Hearts,Spades\}[/tex]
a) Getting a 7 and getting a jack:
Since a 7 and a Jack are different rank elements, you either pick a 7 of a suite, or a Jack of a suite, but never both. So, the events are mutually exclusive.
b) Getting a club and getting a king:
Since a Club is a suite and a King is a Rank, the sample space will have a King of Clubs card. So, the events are not mutually exclusive.
c) Getting a face card and getting an ace:
A face card is a card with a face on it. Faces are Ranks, but an Ace is also a Rank. The sample space contains cards with only one Rank per card. So, the events are mutually exclusive.
d) Getting a face card and getting a spade:
Faces are Ranks, and a Spade is a suite. The sample space will contain face cards for the Spade suite of cards. So, the events are not mutually exclusive.
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