In: Statistics and Probability
Hyram has a standard deck of 52 playing cards. The deck contains 4 suits (hearts, diamonds, clubs, and spades), and each suit contains 13 cards labeled 2 through 10, as well as jack, queen, king, and ace.
Four friends are trying to determine some probabilities related to randomly drawing a single card from the deck.
Consider the following events, and then answer the question.
A: drawing a diamond
B: drawing a queen
Which friend provided the correct analysis?
Samantha says the events are overlapping because drawing a card that is a diamond would change the probability of drawing a card that is a queen.
Alexis says the events are overlapping because a card can be both a diamond and a queen at the same time.
Jessica says the events are disjoint because a card cannot be a diamond and a queen at the same time.
Ashley says the events are disjoint because drawing a card that is a diamond would have no effect on the probability of drawing a card that is a queen.
A standard deck of 52 playing cards contains 4 suits (hearts, diamonds, clubs, and spades), and each suit contains 13 cards labeled 2 through 10, as well as jack, queen, king, and ace.
Four friends are trying to determine some probabilities related to randomly drawing a single card from the deck.
Consider the following events, and then answer the question.
A: drawing a diamond
B: drawing a queen
## Sample space (S / OMEGA)=all 52 cards
## n(S)=52
## Sample space for event A is {diamonds cards labeled 2-10,diamond
Jack, diamond Queen, diamond King, diamond Ace}
## n(A)=13
## Therefore, P(A)=n(A)/n(S)=13/52=1/4
## Sample space for event B is {hearts Queen, diamond Queen, clubs
Queen, Spades Queen}
## n(B)=4
## Therefore, P(B)=n(B)/n(S)=4/52=1/13
## Intersection (Overlap) of event(s) is the element which
appears in both the event A as well as B.
## Therefore, intersection of event A and B is "diamond
Queen" i.e. ( A, B )={diamond Queen}.
## "diamond Queen" is a card can be both a
diamond and a queen at the same time.
## Events A and B are disjoint if their intersection is
empty.
## Therefore, events A and B are not disjoint which means that
Jessica and Ashley provide incorrect analysis.
Which friend provided the correct analysis?
Alexis provided the correct analysis.
"Alexis says the events are overlapping because a card can be
both a diamond and a queen at the same time."