## Shue a full deck of cards and turn them over one by one until an Ace appears. It turns out that this happened exactly when the 20th card was

Question

Shue a full deck of cards and turn them over one by one until an Ace appears. It turns out that this happened exactly when the 20th card was turned over. What is the probability that the next card is (a) the ace of spades; (b) the two of clubs

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3 months 2022-02-03T03:50:52+00:00 1 Answer 0 views 0

Step-by-step explanation:

In a standard deck of cards, there 54 cards (52 cards plus 2 Jokers). There are 4 suits (kinds of shapes) in a deck namely: Clubs, Diamonds, Hearts and Spades. Each of the suits numbers from number 2 to number 10 (numbering 36 cards). Afterwards, we have 4 suits each for the Jack, Queen, King & Ace cards (numbering 16 cards). And then 2 Jokers

An Ace turned up at the 20th card, this means there 34 cards left. The number of cards left is given by the difference between 54 & 20. Mathematically shown below:

Cards left = 54 – 20 = 34

Total number of cards = 54, number of Aces of Spades ♠ in the deck = 1, number of two clubs ♣ in the deck = 1

A. Probability of the next card being Ace of Spades ♠ = the number of Ace of Spades card in the deck ÷ Total number of cards left in the deck

Pr (Ace of Spades) = 1 ÷ 34

Pr (Ace of Spades) = 0.0294 or 2.94%

B. Probability of the next card being Two of Clubs ♣ = the number of Two of Clubs card in the deck ÷ Total number of cards left in the deck

Pr (Two of Clubs) = 1 ÷ 34

Pr (Two of Clubs) = 0.0294 or 2.94%

It therefore implies that the chancess of the next card being Ace of Spades (A ♠) or Two of Clubs (2 ♣) is the same; the Ace of Spades is just equally as likely to be picked as the next card from the deck as Two of Clubs