QQuestionMathematics
QuestionMathematics
An ordinary deck of cards contains 52 cards divided into four suits. The red suits are diamonds (♦) and hearts (♥), and the black suits are clubs (♣) and spades (♠). Each suit contains 13 cards of the following denominations: 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king), and A (ace). The cards J, Q, and K are called face cards.
Imagine choosing a card at random from a thoroughly mixed deck. Consider the event that the chosen card is red and has an even number on it. Which of the following expresses this event as a set?
A. {2♦, 4♦, 6♦, 8♦, 10♦, 2♥, 4♥, 6♥, 8♥, 10♥}
B. {2♦, 4♦, 6♦, 8♦, 10♦, 2♥, 4♥, 6♥, 8♥, 10}
C. {2♦, 4a, 6A, 8A, 10A, 24, 44, 64, 84, 104}
D. {24, 44, 6A, 8A, 104, 2♦, 4♦, 6♦, 8♦, 10♥}
E. {24, 44, 6A, 8A, 104, 24, 44, 64, 84, 104, 2♦, 4♦, 6♦, 8♦, 10♦, 2♥, 4♥, 6♥, 8♥, 10♥}
What is the probability of this event?
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Answer
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Step 1: Determine the number of favorable outcomes
The event is choosing a red card with an even number on it. The even-numbered cards in a deck are 2, 4, 6, 8, and 10. There are two red suits, diamonds and hearts, so there are 2 x 5 = 10 favorable outcomes (two suits with five even-numbered cards each).
Final Answer
The event is choosing a red card with an even number on it. The even-numbered cards in a deck are 2, 4, 6, 8, and 10. There are two red suits, diamonds and hearts, so there are 2 x 5 = 10 favorable outcomes (two suits with five even-numbered cards each).
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