Using a standard 52-card deck, find the following probabilities. Leave your answer as a reduced fraction.

Question

Using a standard 52-card deck, find the following probabilities. Leave your answer as a reduced fraction.

1.) If a card is randomly selected, what is the probability that the card is any one suit, e.g., a diamond, heart, spade, or club? 

2.) If two cards are randomly selected, what is the probability of drawing a face card first, followed by drawing a numbered card? 

3.) If two cards are randomly selected, what is the probability of drawing any one suit first, followed by drawing a face card? 

Answer 1

OK, this goes back to the basic rule of probability. The probability P of any event x is equal to the number of ways that event x can occur divided by the total number of ways any event can occur.

P(x) =. s/n. where s = nr. of ways to success and n = number of total outcomes.

52 card deck with 4 suits, 9 numbered cards in each suit (2 - 9), 3 face cards in each suit (jack,queen,king), and an ace (A) in each suit.

1) What is the probability any Given suit will be picked at random from the 52 cards.

Total number of any one suit = 13. (9 numbered cards, 1 ace, and 3 face cards per suit). This is 's'

Total number of cards that could be selected - 52

P(x) = 13/52 or 1/4

2 What is the probability of drawing a face card of any suit, then on the second pull of the deck, get a numbered card.

a) Probability of a face card =. Number of face cards in deck (12) divided by number of cards (52) or P₁ =12/52

b) Probability of a numbered card given a deck with 51 cards, and 36 (4 x 9) numbered cards , assuming the first card was a face card as specified. P₂ = 36/51

Total probability = P₁ * P₂. or 36/221

3 If two cards are randomly selected, what is the probability of drawing any one suit first, followed by drawing a face card? This is calculated similarly to 2

P₁ = 1/4. (see question one)

P₂ = 12/51 or 4/17

answer = P₁ * P₂ or 1/17