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3 cards are taken out of a deck in turn. You win if one of the following events takes place:

i) either the first card is an ace
ii) either the first two cards are figures (J, Q, K)
iii) either the 3 cards belong to the same sequence
Write the complete system of events.

User MstrQKN
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1 Answer

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Final answer:

The complete system of events includes drawing an Ace first, drawing two face cards first, or drawing three cards in a sequence from a standard 52-card deck. Event probabilities vary by the number of available cards for consecutive draws and the specific sequences involved.

Step-by-step explanation:

The question relates to the probability of certain events occurring when drawing cards from a standard 52-card deck. Here are the possible events as per the question's requirements:

  • Event A: The first card drawn is an Ace (Ace of clubs, diamonds, hearts, or spades).
  • Event B: The first two cards drawn are face cards (Jack, Queen, or King of any suit).
  • Event C: The three cards drawn belong to the same sequence (consecutive numbers such as 4, 5, 6 of any suits).

A standard deck of cards has four Aces, therefore the probability of the first card being an Ace (Event A) is 4 out of 52. For Event B, there are 12 face cards, and when drawing without replacement, this affects the total card count and the number of remaining face cards for the second draw. Event C's probability depends on the sequence order - since the cards must be consecutive but can start anywhere from 2 (2,3,4) to 10 (10,J,Q) in a sequence.

To calculate the precise probabilities of these events, further combinatorial analysis is required, considering the non-replacement draws, the sequence card orders, and the available number of face cards when conducting the draws.

User Rsboarder
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