Question

In: Statistics and Probability

Hyram has a standard deck of 52 playing cards. The deck contains 4 suits (hearts, diamonds,...

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.

Solutions

Expert Solution

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."


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