what is the probability of drawing 5 queens from a standard deck of cards?
A standard deck of cards has 4 queens, one from each of the four suits (Spade, Heart, Diamond and Club).
Therefore the event Q of drawing 5 queens does not exist in the sample space Ω.
Therefore probability P(Q) of drawing 5 queens is zero.
Note: the above answer assumes no replacement of cards.
If the question assumes with replacement, then drawing a queen from a full deck has a probability of 13/52=1/13.
In a 4 step random experiment, the probability of getting a queen at each of the four steps is given by (1/13)^4.
Correction:
4/52=1/13
To find the probability of drawing 5 queens from a standard deck of cards, we need to divide the number of favorable outcomes (drawing 5 queens) by the number of possible outcomes (drawing any 5 cards).
Let's break it down step by step:
Step 1: Determine the total number of cards in the deck.
A standard deck of cards has 52 cards.
Step 2: Determine the number of ways to choose 5 cards from a deck of 52 cards.
We use the combination formula to find the number of ways to choose 5 cards from 52.
The formula is nCr = n! / [(n-r)! * r!], where n is the total number of cards and r is the number of cards we want to choose.
nCr = 52! / [(52-5)! * 5!]
Simplifying this expression, we get 52! / 47! * 5!
Canceling out the common terms, we have (52 * 51 * 50 * 49 * 48) / (5 * 4 * 3 * 2 * 1)
This simplifies to 259,896.
Step 3: Determine the number of ways to choose 5 queens from a deck of 4 queens.
Since there are only 4 queens in a standard deck, the number of ways to choose 5 queens is 0.
Step 4: Calculate the probability.
To get the probability, we divide the number of favorable outcomes (0 in this case) by the number of possible outcomes (259,896).
So the probability is 0/259,896, which simplifies to 0.
Therefore, the probability of drawing 5 queens from a standard deck of cards is 0.