in a standard deck of cards there are four suits: spades, clubs, hearts, and diamonds. each suit has one…

in a standard deck of cards there are four suits: spades, clubs, hearts, and diamonds. each suit has one each of 13 cards: ace, king, queen, jack, 2, 3, 4, 5, 6, 7, 8, 9, and 10. if event a is choosing a king, event b is choosing a heart, and event c is choosing a jack, which venn diagram could represent this description?

in a standard deck of cards there are four suits: spades, clubs, hearts, and diamonds. each suit has one each of 13 cards: ace, king, queen, jack, 2, 3, 4, 5, 6, 7, 8, 9, and 10. if event a is choosing a king, event b is choosing a heart, and event c is choosing a jack, which venn diagram could represent this description?

Answer

Answer:

We need to analyze the relationships between the events to determine the Venn - diagram.

  1. There are 4 kings in a deck (one in each suit), 13 hearts in a deck, and 4 jacks in a deck.
    • The event of choosing a king and the event of choosing a heart have an overlap because there is 1 king of hearts. So the circle representing event A (choosing a king) and the circle representing event B (choosing a heart) should intersect.
    • The event of choosing a king and the event of choosing a jack have no overlap since a card cannot be both a king and a jack. So the circle representing event A (choosing a king) and the circle representing event C (choosing a jack) should not intersect.
    • The event of choosing a jack and the event of choosing a heart have an overlap because there is 1 jack of hearts. So the circle representing event C (choosing a jack) and the circle representing event B (choosing a heart) should intersect. We would look for a Venn - diagram with three circles (A for king, B for heart, C for jack) where A and B intersect, B and C intersect, and A and C do not intersect.

Explanation:

Step1: Analyze event A and B relationship

There is a king of hearts, so they intersect.

Step2: Analyze event A and C relationship

A card can't be king and jack, so no intersection.

Step3: Analyze event B and C relationship

There is a jack of hearts, so they intersect.